This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic fie...This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.展开更多
The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove...The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.展开更多
We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably sm...We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.展开更多
This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time unifo...This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.展开更多
In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimension...In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.展开更多
The authors prove two global existence results of strong solutions of the isentropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And th...The authors prove two global existence results of strong solutions of the isentropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.展开更多
In this paper, we consider the viscous, micropolar, compressible flow in one dimension. We give the proof of existence and uniqueness of strong solutions for the initial boundary problem that vacuum can be allowed ini...In this paper, we consider the viscous, micropolar, compressible flow in one dimension. We give the proof of existence and uniqueness of strong solutions for the initial boundary problem that vacuum can be allowed initially.展开更多
We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ（ρ） = Aρα, where α〉 0 and A 〉0. The global existence of strong solutions is...We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ（ρ） = Aρα, where α〉 0 and A 〉0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.展开更多
This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be converg...This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.展开更多
In this paper,the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data.The global existence and un...In this paper,the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data.The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs'regularization method.展开更多
The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if t...The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.展开更多
In this paper,we mainly investigate the Cauchy problem for the 3D incompressible magnetohydrodynamic(MHD)equations with damping terms.Under a certain smallness assumption on the initial data,this paper not only establ...In this paper,we mainly investigate the Cauchy problem for the 3D incompressible magnetohydrodynamic(MHD)equations with damping terms.Under a certain smallness assumption on the initial data,this paper not only establishes the global existence of strong solutions to the equations when parameters satisfy 1≤α,β<3,but also obtains the decay estimates of the solutions to the MHD equations.展开更多
This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" cond...This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.展开更多
The Cauchy problem for non-isentropic compressible Navier-Stokes/Allen-Cahn system with degenerate heat-conductivityκ(θ)=κθ^(β)in 1-D is discussed in this paper.This system is widely used to describe the motion o...The Cauchy problem for non-isentropic compressible Navier-Stokes/Allen-Cahn system with degenerate heat-conductivityκ(θ)=κθ^(β)in 1-D is discussed in this paper.This system is widely used to describe the motion of immiscible two-phase flow with diffused interface.The well-posedness for strong solution of this problem is established with the H^(1)initial data for density,temperature,velocity,and the H^(2)initial data for phase field.The result shows that no discontinuity of the phase field,vacuum,shock wave,mass or heat concentration will be developed at any finite time in the whole space.From the hydrodynamic point of view,this means that no matter how complex the interaction between the hydrodynamic and phase-field effects,phase separation will not occur,but the phase transition is possible.展开更多
基金supported by the National Natural Science Foundation of China(12401279,12371219)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027).
文摘This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.
文摘The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.
基金supported by National Natural Science Foundation of China(11701193,11671086)Natural Science Foundation of Fujian Province(2018J05005,2017J01562)+3 种基金Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan(2017ZT012)supported by National Natural Science Foundation of China(11901474)the Chongqing Talent Plan for Young Topnotch Talents(CQYC202005074)the Innovation Support Program for Chongqing Overseas Returnees(cx2020082).
文摘We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.
基金partially supported by the National Natural Science Foundation of China(11701192)。
文摘This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.
文摘In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.
基金the National Natural Science Foundation of China (No.10531020)the Program of 985 Innovation Engineering on Information in Xiamen University (2004-2007)the New Century Excellent Talents in Xiamen University
文摘The authors prove two global existence results of strong solutions of the isentropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.
文摘In this paper, we consider the viscous, micropolar, compressible flow in one dimension. We give the proof of existence and uniqueness of strong solutions for the initial boundary problem that vacuum can be allowed initially.
基金supported by the National Natural Science Foundation of China under Grant No.11301244the Foundation of Education Department of Liaoning Province of China under Grant L2013006+1 种基金the Doctor Startup Foundation of Liaoning Province of China Grant 20131040supported by the National Natural Science Foundation of China under Grant No.11371297
文摘We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ（ρ） = Aρα, where α〉 0 and A 〉0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.
基金partially supported by the NSFC(11421061,12271507)the Natural Science Foundation of Shanghai(15ZR1403900)。
文摘This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.
基金the NSFC(11571046,11671225)the ISF-NSFC joint research program NSFC(11761141008)the BJNSF(1182004)。
文摘In this paper,the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data.The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs'regularization method.
基金Project supported by the National Natural Science Foundation of China (No.90511009)
文摘The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.
基金supported by the National Natural Science Foundation of China(Grant No.12301269)the Guangzhou Municipal Science and Technology Project(Grant No.2025A04J5086).
文摘In this paper,we mainly investigate the Cauchy problem for the 3D incompressible magnetohydrodynamic(MHD)equations with damping terms.Under a certain smallness assumption on the initial data,this paper not only establishes the global existence of strong solutions to the equations when parameters satisfy 1≤α,β<3,but also obtains the decay estimates of the solutions to the MHD equations.
基金supported by National Natural Science Foundation of China (Grant No. 11471334)Program for New Century Excellent Talents in University (Grant No. NCET-12-0085)
文摘This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.
基金supported by the National Natural Science Foundation of China(Nos.12471207,12371434,12171024)the National Key R&D Program of China Under Grant(No.2022YFE03040002)。
文摘The Cauchy problem for non-isentropic compressible Navier-Stokes/Allen-Cahn system with degenerate heat-conductivityκ(θ)=κθ^(β)in 1-D is discussed in this paper.This system is widely used to describe the motion of immiscible two-phase flow with diffused interface.The well-posedness for strong solution of this problem is established with the H^(1)initial data for density,temperature,velocity,and the H^(2)initial data for phase field.The result shows that no discontinuity of the phase field,vacuum,shock wave,mass or heat concentration will be developed at any finite time in the whole space.From the hydrodynamic point of view,this means that no matter how complex the interaction between the hydrodynamic and phase-field effects,phase separation will not occur,but the phase transition is possible.
