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
Initial residual stress is the main reason causing machining deformation of the workpiece,which has been deemed as one of the most important aspects of machining quality issues.The inference of the distribution of ini...Initial residual stress is the main reason causing machining deformation of the workpiece,which has been deemed as one of the most important aspects of machining quality issues.The inference of the distribution of initial residual stress inside the blank has significant meaning for machining deformation control.Due to the principle error of existing residual stress detection methods,there are still challenges in practical applications.Aiming at the detection problem of the initial residual stress field,an initial residual stress inference method by incorporating monitoring data and mechanism model is proposed in this paper.Monitoring data during machining process is used to represent the macroscopic characterization of the unbalanced residual stress,and the finite element numerical model is used as the mechanism model so as to solve the problem that the analytic mechanism model is difficult to establish;the policy gradient approach is introduced to solve the gradient descent problem of the combination of learning model and mechanism model.Finally,the initial residual stress field is obtained through iterative calculation based on the fusing method of monitoring data and mechanism model.Verification results show that the proposed inference method of initial residual stress field can accurately and effectively reflect the machining deformation in the actual machining process.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 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
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 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
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
The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
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
The 2002/03 El Ni？o event, a new type of El Ni？o with maximum warm anomaly occurring in the central equatorial Pacific, is known as central-Pacific（CP） El Ni？o. In this study, on the basis of an El Ni？o predicti...The 2002/03 El Ni？o event, a new type of El Ni？o with maximum warm anomaly occurring in the central equatorial Pacific, is known as central-Pacific（CP） El Ni？o. In this study, on the basis of an El Ni？o prediction system, roles of the initial ocean surface and subsurface states on predicting the 2002/03 CP El Ni？o event are investigated to determine conditions favorable for predicting El Ni？o growth and are isolated in three sets of hindcast experiments. The hindcast is initialized through assimilation of only the sea surface temperature（SST）observations to optimize the initial surface condition（Assim_SST）, only the sea level（SL） data to update the initial subsurface state（Assim_SL）, or both the SST and SL data（Assim_SST＋SL）. Results highlight that the hindcasts with three different initial states all can successfully predict the 2002/03 El Ni？o event one year in advance and that the Assim_SST＋SL hindcast performs best. A comparison between the various sets of hindcast results further demonstrates that successful prediction is significantly affected by both of the initial surface and subsurface conditions, but in different developing phases of the 2002/03 El Ni？o event. The accurate initial surface state can easier trigger the prediction of the 2002/03 El Ni？o, whereas a more reasonable initial subsurface state can contribute to improving the prediction in the growth of the warm event.展开更多
In this study, two deep convective cloud cases were analyzed in detail to study their initiation and evolution. In both cases, all deep convective clouds were positioned at the rear of the cold front cloud bands and p...In this study, two deep convective cloud cases were analyzed in detail to study their initiation and evolution. In both cases, all deep convective clouds were positioned at the rear of the cold front cloud bands and propagated backward. Satellite data showed that prior to initiation of the deep convective clouds, thermodynamic and moist conditions were favorable for their formation. In the morning, a deep convective cloud at the rear of cold front cloud band propagated backward, the outflow boundary of which created favorable conditions for initiation. An additional deep convective cloud cluster moved in from the west and interacted with the outflow boundary to develop a mesoscale convective system(MCS) with large, ellipse-shaped deep convective clouds that brought strong rainfall. The initiation and evolution of these clouds are shown clearly in satellite data and provide significant information for nowcasting and short-term forecasting.展开更多
For the short pulse initial data with a first-order outgoing constraint condition and optimal orders of smallness,we establish the global existence of smooth solutions to 2D quasilinear wave equations with higher-orde...For the short pulse initial data with a first-order outgoing constraint condition and optimal orders of smallness,we establish the global existence of smooth solutions to 2D quasilinear wave equations with higher-order null conditions.Such kinds of wave equations include 2D relativistic membrane equations,2D membrane equations,and some 2D quasilinear equations which come from the nonlinear Maxwell equations in electromagnetic theory or from the corresponding Lagrangian functionals as perturbations of the Lagrangian densities of linear wave operators.The main ingredients of the analysis here include looking for a new good unknown,finding some key identities based on the higher-order null conditions and the resulting null frames,as well as overcoming the difficulties due to the slow decay of solutions to the 2D wave equation,so that the solutions can be estimated precisely.展开更多
Extensive oedometer tests and physical tests have been conducted on remolded and reconstituted marine soils with different initial water contents and liquid limits. The oedometer test data can be well fitted with a st...Extensive oedometer tests and physical tests have been conducted on remolded and reconstituted marine soils with different initial water contents and liquid limits. The oedometer test data can be well fitted with a straight line in the bilogarithmic ln(1+ e ) ～ lg p plot. The initial effective stress corresponding to the initial void ratio is determined by extrapolation of the bilogarithmic compression line. This new way of extrapolating oedometer test data to the initial void ratio overcomes the difficulty of measuring the residual effective stress of soils in the remolded state. The initial stable compression line of ocean floor deposits under different deposition environments corresponds to the compression line at the sensitivity equal to one. This initial stable compression line obtained in this study is consistent with the available compression line at the sensitivity equal to one which is proposed based on the experimental data of remolded undrained strength and the theoretical concept of Cam clay critical state line.展开更多
With the rapid development of lnternet technology, the volume of data has increased exponentially. As the large amounts of data are no longer easy to be managed and secured by the owners, big data security and privacy...With the rapid development of lnternet technology, the volume of data has increased exponentially. As the large amounts of data are no longer easy to be managed and secured by the owners, big data security and privacy has become a hot issue. One of the most popular research fields for solving the data security and data privacy is within the scope of big data governance and security, In this paper, we introduce the basic concepts of data governance and security. Then, all the state-of-the-art open source frameworks for data governance and security, including Apache Falcon, Apache Atlas, Apache Ranger, Apache Sentry and Kerberos, are detailed and discussed with descriptions of their implementation principles and possible applications.展开更多
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
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National Natural Science Foundation of China(Grant No.51775278)National Science Fund of China for Distinguished Young Scholars(Grant No.51925505).
文摘Initial residual stress is the main reason causing machining deformation of the workpiece,which has been deemed as one of the most important aspects of machining quality issues.The inference of the distribution of initial residual stress inside the blank has significant meaning for machining deformation control.Due to the principle error of existing residual stress detection methods,there are still challenges in practical applications.Aiming at the detection problem of the initial residual stress field,an initial residual stress inference method by incorporating monitoring data and mechanism model is proposed in this paper.Monitoring data during machining process is used to represent the macroscopic characterization of the unbalanced residual stress,and the finite element numerical model is used as the mechanism model so as to solve the problem that the analytic mechanism model is difficult to establish;the policy gradient approach is introduced to solve the gradient descent problem of the combination of learning model and mechanism model.Finally,the initial residual stress field is obtained through iterative calculation based on the fusing method of monitoring data and mechanism model.Verification results show that the proposed inference method of initial residual stress field can accurately and effectively reflect the machining deformation in the actual machining process.
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.
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.
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.
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 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The National Program for Support of Top-notch Young Professionalsthe Project of Global Change and Air-Sea Interaction+1 种基金the National Basic Research Program(973 Program)of China under contract No.2012CB417404the Project"Western Pacific Ocean System:Structure,Dynamics and Consequences"(WPOS)of Chinese Academy Sciences under contract No.XDA10010405
文摘The 2002/03 El Ni？o event, a new type of El Ni？o with maximum warm anomaly occurring in the central equatorial Pacific, is known as central-Pacific（CP） El Ni？o. In this study, on the basis of an El Ni？o prediction system, roles of the initial ocean surface and subsurface states on predicting the 2002/03 CP El Ni？o event are investigated to determine conditions favorable for predicting El Ni？o growth and are isolated in three sets of hindcast experiments. The hindcast is initialized through assimilation of only the sea surface temperature（SST）observations to optimize the initial surface condition（Assim_SST）, only the sea level（SL） data to update the initial subsurface state（Assim_SL）, or both the SST and SL data（Assim_SST＋SL）. Results highlight that the hindcasts with three different initial states all can successfully predict the 2002/03 El Ni？o event one year in advance and that the Assim_SST＋SL hindcast performs best. A comparison between the various sets of hindcast results further demonstrates that successful prediction is significantly affected by both of the initial surface and subsurface conditions, but in different developing phases of the 2002/03 El Ni？o event. The accurate initial surface state can easier trigger the prediction of the 2002/03 El Ni？o, whereas a more reasonable initial subsurface state can contribute to improving the prediction in the growth of the warm event.
基金supported by the National Natural Science Foundation of China"Study of Characteristics of the Environmental Field before the Deep Convective Cloud Initiated Using Geostational Meteorological Satellite Data"(Grant No.41005026)
文摘In this study, two deep convective cloud cases were analyzed in detail to study their initiation and evolution. In both cases, all deep convective clouds were positioned at the rear of the cold front cloud bands and propagated backward. Satellite data showed that prior to initiation of the deep convective clouds, thermodynamic and moist conditions were favorable for their formation. In the morning, a deep convective cloud at the rear of cold front cloud band propagated backward, the outflow boundary of which created favorable conditions for initiation. An additional deep convective cloud cluster moved in from the west and interacted with the outflow boundary to develop a mesoscale convective system(MCS) with large, ellipse-shaped deep convective clouds that brought strong rainfall. The initiation and evolution of these clouds are shown clearly in satellite data and provide significant information for nowcasting and short-term forecasting.
基金supported by National Natural Science Foundation of China(Grant Nos.12331007 and 12071223)supported by the Zheng Ge Ru Foundation,Hong Kong RGC Earmarked Research(Grant Nos.CUHK-14301421,CUHK-14300819,CUHK-14302819 and CUHK-14301023)+1 种基金Basic and Applied Basic Research Foundations of Guangdong Province(Grant No.2020131515310002)the Key Projects of National Natural Science Foundation of China(Grant Nos.12131010 and 11931013).
文摘For the short pulse initial data with a first-order outgoing constraint condition and optimal orders of smallness,we establish the global existence of smooth solutions to 2D quasilinear wave equations with higher-order null conditions.Such kinds of wave equations include 2D relativistic membrane equations,2D membrane equations,and some 2D quasilinear equations which come from the nonlinear Maxwell equations in electromagnetic theory or from the corresponding Lagrangian functionals as perturbations of the Lagrangian densities of linear wave operators.The main ingredients of the analysis here include looking for a new good unknown,finding some key identities based on the higher-order null conditions and the resulting null frames,as well as overcoming the difficulties due to the slow decay of solutions to the 2D wave equation,so that the solutions can be estimated precisely.
文摘Extensive oedometer tests and physical tests have been conducted on remolded and reconstituted marine soils with different initial water contents and liquid limits. The oedometer test data can be well fitted with a straight line in the bilogarithmic ln(1+ e ) ～ lg p plot. The initial effective stress corresponding to the initial void ratio is determined by extrapolation of the bilogarithmic compression line. This new way of extrapolating oedometer test data to the initial void ratio overcomes the difficulty of measuring the residual effective stress of soils in the remolded state. The initial stable compression line of ocean floor deposits under different deposition environments corresponds to the compression line at the sensitivity equal to one. This initial stable compression line obtained in this study is consistent with the available compression line at the sensitivity equal to one which is proposed based on the experimental data of remolded undrained strength and the theoretical concept of Cam clay critical state line.
文摘With the rapid development of lnternet technology, the volume of data has increased exponentially. As the large amounts of data are no longer easy to be managed and secured by the owners, big data security and privacy has become a hot issue. One of the most popular research fields for solving the data security and data privacy is within the scope of big data governance and security, In this paper, we introduce the basic concepts of data governance and security. Then, all the state-of-the-art open source frameworks for data governance and security, including Apache Falcon, Apache Atlas, Apache Ranger, Apache Sentry and Kerberos, are detailed and discussed with descriptions of their implementation principles and possible applications.
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.
