We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the globa...We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the global existence and uniqueness of strong solutions.In particular,the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support.展开更多
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where...In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.展开更多
We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-...We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5.展开更多
In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetr...In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.展开更多
A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and ...A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.展开更多
In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an ele...In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).展开更多
In this paper,we study the large-time behavior of periodic solutions for parabolic conservation laws.There is no smallness assumption on the initial data.We firstly get the local existence of the solution by the itera...In this paper,we study the large-time behavior of periodic solutions for parabolic conservation laws.There is no smallness assumption on the initial data.We firstly get the local existence of the solution by the iterative scheme,then we get the exponential decay estimates for the solution by energy method and maximum principle,and obtain the global solution in the same time.展开更多
The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
The incompressible limit of nonisentropic ideal magnetohydrodynamic equations with general initial data in the whole space R^(3) is proved in this paper.The uniform estimates of solutions with respect to the Mach numb...The incompressible limit of nonisentropic ideal magnetohydrodynamic equations with general initial data in the whole space R^(3) is proved in this paper.The uniform estimates of solutions with respect to the Mach number are obtained by using energy estimate.Strong convergence results of the smooth solutions are established by using Strichartz's estimates in the whole space.展开更多
This paper studies an epidemic model with nonlocal dispersals.We focus on the influences of initial data and nonlocal dispersals on its spatial propagation.Here,initial data stand for the spatial concentrations of the...This paper studies an epidemic model with nonlocal dispersals.We focus on the influences of initial data and nonlocal dispersals on its spatial propagation.Here,initial data stand for the spatial concentrations of the infectious agent and the infectious human population when the epidemic breaks out and the nonlocal dispersals mean their diffusion strategies.Two types of initial data decaying to zero exponentially or faster are considered.For the first type,we show that spreading speeds are two constants whose signs change with the number of elements in some set.Moreover,we find an interesting phenomenon:the asymmetry of nonlocal dispersals can influence the propagating directions of the solutions and the stability of steady states.For the second type,we show that the spreading speed is decreasing with respect to the exponentially decaying rate of initial data,and further,its minimum value coincides with the spreading speed for the first type.In addition,we give some results about the nonexistence of traveling wave solutions and the monotone property of the solutions.Finally,some applications are presented to illustrate the theoretical results.展开更多
We study the Ll-error of a Hamiltonian-preserving scheme, developed in [19], for the Liouville equation with a piecewise constant potential in one space dimension when the initial data is given with perturbation error...We study the Ll-error of a Hamiltonian-preserving scheme, developed in [19], for the Liouville equation with a piecewise constant potential in one space dimension when the initial data is given with perturbation errors. We extend the l1-stability analysis in [46] and apply the Ll-error estimates with exact initial data established in [45] for the same scheme. We prove that the scheme with the Dirichlet incoming boundary conditions and for a class of bounded initial data is Ll-convergent when the initial data is given with a wide class of perturbation errors, and derive the Ll-error bounds with explicit coefficients. The convergence rate of the scheme is shown to be less than the order of the initial perturbation error, matching with the fact that the perturbation solution can be l1-unstable.展开更多
The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained ...The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained for the power of Laplacian α∈[1/2,1).展开更多
This paper mainly concerns the mathematical justification of the asymptotic limit of the GrossPitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of...This paper mainly concerns the mathematical justification of the asymptotic limit of the GrossPitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.展开更多
This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value.The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitt...This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value.The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface,with piecewise linear approximation to the interface.The semi-discrete finite element problem is furthermore discretized in time by the k-step backward difference formula with k=1,...,6.To maintain high-order convergence in time for possibly nonsmooth L 2 initial value,we modify the standard backward difference formula at the first k−1 time levels by using a method recently developed for fractional evolution equations.An error bound of O(t−k nτk+t−1 n h 2|log h|)is established for the fully discrete finite element method for general L 2 initial data.展开更多
In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions t...In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.展开更多
In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We gi...In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We give the relation between the viscosity coefficients and the initial energy,which implies that the Cauchy problem under consideration has a global classical solution.展开更多
We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating s...We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating sequences generatedby the method of vanishing viscosity. The uniqueness of the generalized solutions whichcan be obtained by the method of vanishing viscosity is also obtained.展开更多
In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element i...In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element is used for the velocity and pressure and linear polynomial for the temperature.The time discretization is based on the Crank-Nicolson scheme.In order to simplify the computations,the nonlinear terms are treated by the explicit scheme.The advantages of our numerical scheme can be list as follows:(1)The original problem is split into two linear subproblems,these subproblems can be solved in each time level in parallel and the computational sizes are smaller than the origin one.(2)A constant coefficient linear discrete algebraic system is obtained in each subproblem and the computation becomes easy.The main contributions of this work are the stability and convergence results of numerical solutions with nonsmooth initial data.Finally,some numerical results are presented to verify the established theoretical results and show the performances of the developed numerical scheme.展开更多
Method development has always been and will continue to be a core driving force of microbiome science, In this perspective, we argue that in the next decade, method development in microbiome analysis will be driven by...Method development has always been and will continue to be a core driving force of microbiome science, In this perspective, we argue that in the next decade, method development in microbiome analysis will be driven by three key changes in both ways of thinking and technological platforms： ① a shift from dissecting microbiota structure by sequencing to tracking microbiota state, function, and intercellular interaction via imaging; ② a shift from interrogating a consortium or population of cells to probing individual cells; and ③a shift from microbiome data analysis to microbiome data science. Some of the recent methoddevelopment efforts by Chinese microbiome scientists and their international collaborators that underlie these technological trends are highlighted here. It is our belief that the China Microbiome Initiative has the opportunity to deliver outstanding ＂Made-in-China＂ tools to the international research community, by building an ambitious, competitive, and collaborative program at the forefront of method development for microbiome science.展开更多
This paper is concerned with the large-time behavior of solutions to the Cauchy problem of a one-dimensional viscous radiative and reactive gas.Based on the elaborate energy estimates,we develop a new approach to deri...This paper is concerned with the large-time behavior of solutions to the Cauchy problem of a one-dimensional viscous radiative and reactive gas.Based on the elaborate energy estimates,we develop a new approach to derive the upper bound of the absolute temperature by avoiding the use of auxiliary functions Z(t)and W(t)introduced by Liao and Zhao[J.Differential Equations,2018,265(5):2076-2120].Our results also improve upon the results obtained in Liao and Zhao[J.Differential Equations,2018,265(5):2076-2120].展开更多
文摘We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the global existence and uniqueness of strong solutions.In particular,the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support.
基金supported by the National Natural Science Foundation of China under Grant No.12147115the Discipline(Subject)Leader Cultivation Project of Universities in Anhui Province under Grant Nos.DTR2023052 and DTR2024046+2 种基金the Natural Science Research Project of Universities in Anhui Province under Grant No.2024AH040202the Young Top Notch Talents and Young Scholars of High End Talent Introduction and Cultivation Action Project in Anhui Provincethe Scientific Research Foundation Funded Project of Chuzhou University under Grant Nos.2022qd022 and 2022qd038。
文摘In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.
基金supported by the NationalNatural Science Foundation of China(12001236)the Natural Science Foundation of Guangdong Province(2020A1515110494)。
文摘We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5.
基金Supported by CNPq-Conselho Nacional de Desenvolvimento Cient'fico e Tecnológico
文摘In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.
基金partially the National Key R&D Program of China(2022YFA1007300)the NSFC(11901386,12031013)+2 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(XDA25010403)the NSFC(11801194,11971188)the Hubei Key Laboratory of Engineering Modeling and Scientific Computing。
文摘A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.
文摘In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).
基金Foundation item： Supported by the National Science Foundation of China（1107116）
文摘In this paper,we study the large-time behavior of periodic solutions for parabolic conservation laws.There is no smallness assumption on the initial data.We firstly get the local existence of the solution by the iterative scheme,then we get the exponential decay estimates for the solution by energy method and maximum principle,and obtain the global solution in the same time.
文摘The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
基金supported by the NSFC(Grants 12131007 and 12071044).
文摘The incompressible limit of nonisentropic ideal magnetohydrodynamic equations with general initial data in the whole space R^(3) is proved in this paper.The uniform estimates of solutions with respect to the Mach number are obtained by using energy estimate.Strong convergence results of the smooth solutions are established by using Strichartz's estimates in the whole space.
基金supported by China Postdoctoral Science Foundation(Grant No.2019M660047)supported by National Natural Science Foundation of China(Grant Nos.11731005 and 11671180)supported by National Science Foundation of USA(Grant No.DMS-1853622)。
文摘This paper studies an epidemic model with nonlocal dispersals.We focus on the influences of initial data and nonlocal dispersals on its spatial propagation.Here,initial data stand for the spatial concentrations of the infectious agent and the infectious human population when the epidemic breaks out and the nonlocal dispersals mean their diffusion strategies.Two types of initial data decaying to zero exponentially or faster are considered.For the first type,we show that spreading speeds are two constants whose signs change with the number of elements in some set.Moreover,we find an interesting phenomenon:the asymmetry of nonlocal dispersals can influence the propagating directions of the solutions and the stability of steady states.For the second type,we show that the spreading speed is decreasing with respect to the exponentially decaying rate of initial data,and further,its minimum value coincides with the spreading speed for the first type.In addition,we give some results about the nonexistence of traveling wave solutions and the monotone property of the solutions.Finally,some applications are presented to illustrate the theoretical results.
文摘We study the Ll-error of a Hamiltonian-preserving scheme, developed in [19], for the Liouville equation with a piecewise constant potential in one space dimension when the initial data is given with perturbation errors. We extend the l1-stability analysis in [46] and apply the Ll-error estimates with exact initial data established in [45] for the same scheme. We prove that the scheme with the Dirichlet incoming boundary conditions and for a class of bounded initial data is Ll-convergent when the initial data is given with a wide class of perturbation errors, and derive the Ll-error bounds with explicit coefficients. The convergence rate of the scheme is shown to be less than the order of the initial perturbation error, matching with the fact that the perturbation solution can be l1-unstable.
基金Project supported by the National Natural Science Foundation of China (No. 11071162)the Shanghai Jiao Tong University Innovation Fund for Postgraduates (No. WS3220507101)
文摘The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained for the power of Laplacian α∈[1/2,1).
基金supported by National Natural Science Foundation of China(Grant No.11271184)China Scholarship Council,the Priority Academic Program Development of Jiangsu Higher Education Institutions,the Tsz-Tza Foundation,and Ministry of Science and Technology(Grant No.104-2628-M-006-003-MY4)
文摘This paper mainly concerns the mathematical justification of the asymptotic limit of the GrossPitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.
文摘This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value.The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface,with piecewise linear approximation to the interface.The semi-discrete finite element problem is furthermore discretized in time by the k-step backward difference formula with k=1,...,6.To maintain high-order convergence in time for possibly nonsmooth L 2 initial value,we modify the standard backward difference formula at the first k−1 time levels by using a method recently developed for fractional evolution equations.An error bound of O(t−k nτk+t−1 n h 2|log h|)is established for the fully discrete finite element method for general L 2 initial data.
基金supported by National Natural Science Foundation of China(Grant Nos.11971477,11761141008,11601128 and 11671319)the Fundamental Research Funds for the Central Universities+3 种基金the Research Funds of Renmin University of China(Grant No.18XNLG30)Beijing Natural Science Foundation(Grant No.1182007)Doctor Fund of Henan Polytechnic University(Grant No.B2016-57)completed when Yaobin Ou visited Brown University under the support of the China Scholarship Council(Grant No.201806365010)。
文摘In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.
基金supported by National Natural Science Foundation of China (Grant Nos.11001090 and 10971171)the Fundamental Research Funds for the Central Universities (Grant No.11QZR16)
文摘In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We give the relation between the viscosity coefficients and the initial energy,which implies that the Cauchy problem under consideration has a global classical solution.
文摘We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating sequences generatedby the method of vanishing viscosity. The uniqueness of the generalized solutions whichcan be obtained by the method of vanishing viscosity is also obtained.
文摘In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element is used for the velocity and pressure and linear polynomial for the temperature.The time discretization is based on the Crank-Nicolson scheme.In order to simplify the computations,the nonlinear terms are treated by the explicit scheme.The advantages of our numerical scheme can be list as follows:(1)The original problem is split into two linear subproblems,these subproblems can be solved in each time level in parallel and the computational sizes are smaller than the origin one.(2)A constant coefficient linear discrete algebraic system is obtained in each subproblem and the computation becomes easy.The main contributions of this work are the stability and convergence results of numerical solutions with nonsmooth initial data.Finally,some numerical results are presented to verify the established theoretical results and show the performances of the developed numerical scheme.
基金We are grateful to the support from the National Natural Science Foundation of China （NSFC） （31425002, 91231205, 81430011, 61303161, 31470220, and 31327001）, and the Frontier Science Research Program, the Soil-Microbe System Function and Regulation Program, and the Science and Technology Service Network Initiative （STS） from the Chinese Academy of Sciences （CAS）.
文摘Method development has always been and will continue to be a core driving force of microbiome science, In this perspective, we argue that in the next decade, method development in microbiome analysis will be driven by three key changes in both ways of thinking and technological platforms： ① a shift from dissecting microbiota structure by sequencing to tracking microbiota state, function, and intercellular interaction via imaging; ② a shift from interrogating a consortium or population of cells to probing individual cells; and ③a shift from microbiome data analysis to microbiome data science. Some of the recent methoddevelopment efforts by Chinese microbiome scientists and their international collaborators that underlie these technological trends are highlighted here. It is our belief that the China Microbiome Initiative has the opportunity to deliver outstanding ＂Made-in-China＂ tools to the international research community, by building an ambitious, competitive, and collaborative program at the forefront of method development for microbiome science.
基金National Postdoctoral Program for Innovative Talents of China(BX20180054).
文摘This paper is concerned with the large-time behavior of solutions to the Cauchy problem of a one-dimensional viscous radiative and reactive gas.Based on the elaborate energy estimates,we develop a new approach to derive the upper bound of the absolute temperature by avoiding the use of auxiliary functions Z(t)and W(t)introduced by Liao and Zhao[J.Differential Equations,2018,265(5):2076-2120].Our results also improve upon the results obtained in Liao and Zhao[J.Differential Equations,2018,265(5):2076-2120].
