In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary a...In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free-moving boundary. The global existence and uniqueness of strong solutions are established, and the long-time convergence to the equilibrium state is shown to be either at an exponential rate for the horizontal periodic domain or at an algebraic rate for the horizontal whole space.展开更多
A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of...A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.展开更多
This paper is concerned with a diffuse interface model called Navier-Stokes/CahnHilliard system.This model is usually used to describe the motion of immiscible two-phase flows with a diffusion interface.For the period...This paper is concerned with a diffuse interface model called Navier-Stokes/CahnHilliard system.This model is usually used to describe the motion of immiscible two-phase flows with a diffusion interface.For the periodic boundary value problem of this system in torus T3,we prove that there exists a global unique strong solution near the phase separation state,which means that no vacuum,shock wave,mass concentration,interface collision or rupture will be developed in finite time.Furthermore,we establish the large time behavior of the global strong solution of this system.In particular,we find that the phase field decays algebraically to the phase separation state.展开更多
In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space...In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of Schonbek and the spectrum analysis method, and for the high frequency part, we use the global energy estimate and the behavior of exponentially decay operator.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
In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows.
Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is prove...Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is proved that the solutions of (1) tend to those of the following nonlinear parabolic equation time-asymptotically:展开更多
Abstract In this paper, we study the stability of solutions of the Cauchy problem for 1-D compressible Narvier- Stokes equations with general initial data. The asymptotic limit of solution is found, under some conditi...Abstract In this paper, we study the stability of solutions of the Cauchy problem for 1-D compressible Narvier- Stokes equations with general initial data. The asymptotic limit of solution is found, under some conditions. The results in this paper imply the case that the limit function of solution as t → ee is a viscous contact wave in the sense, which approximates the contact discontinuity on any finite-time interval as the heat conduction coefficients toward zero. As a by-product, the decay rates of the solution for the fast diffusion equations are also obtained. The proofs are based on the elementary energy method and the study of asymptotic behavior of the solution to the fast diffusion equation.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 is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under ...This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ｜｜·｜｜H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ｜｜·｜｜H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.展开更多
The purpose of this paper is t0 investigate an irreversible model in the kine-tics of heterogeneous cataIytic reaction-diffusion. The existence, uniqueness andlarge-time behavior of solutions are proved. Particularly,...The purpose of this paper is t0 investigate an irreversible model in the kine-tics of heterogeneous cataIytic reaction-diffusion. The existence, uniqueness andlarge-time behavior of solutions are proved. Particularly, the result shows thatthe reaction ceare in nnite time provided there is some kinds of absorption.展开更多
The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered re...The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered respectively. The global existence of smooth solutions to the IBVP problems for two systems are proved, and their large-time behavior is analyzed. The time-asymptotic equivalence of these two systems are investigated, the decay rate of the difference of solutions between these two systems are shown to be determined explicitly by the initial perturbations and boundary effects. It is found that the oscillation of the specific volume can be cancelled by that of entropy, i.e., the oscillation of the specific volume and entropy is not required to be small.展开更多
In this paper,we investigate the non-autonomous Hamilton-Jacobi equation{ə_(t)u+H(t,x,ə_(x)=0,u(x,t)_(0))=φ(x),x∈M where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We o...In this paper,we investigate the non-autonomous Hamilton-Jacobi equation{ə_(t)u+H(t,x,ə_(x)=0,u(x,t)_(0))=φ(x),x∈M where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_(0))^(t)φ(x)and show T_(t_(0))^(t)φ(x)converges uniformly to a time-periodic viscosity solution u^(*)(x,t)ofə_(t)u+H(t,x,ə_(x)u,u)=0.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11931010, 12226326, and 12226327)supported by National Natural Science Foundation of China (Grant No. 11701053)+2 种基金the Key Research Project of Academy for Multidisciplinary Studies, Capital Normal Universitythe Capacity Building for Sci-Tech Innovation—Fundamental Scientific Research Funds (Grant No. 007/20530290068)the Fundamental Research Funds for the Central Universities (Grant Nos. 0903005203477, 2020CDJQY-A040, and 2020CDJQY-Z001)。
文摘In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free-moving boundary. The global existence and uniqueness of strong solutions are established, and the long-time convergence to the equilibrium state is shown to be either at an exponential rate for the horizontal periodic domain or at an algebraic rate for the horizontal whole space.
基金The first author was supported by the China Postdoctoral Science Foundation(2005037318)The second author acknowledges partial support from the Austrian-Chinese Scientific-Technical Collaboration Agreement, the CTS of Taiwanthe Wittgenstein Award 2000 of P.A. Markowich, funded by the Austrian FWF, the Grants-in-Aid of JSPS No.14-02036the NSFC(10431060)the Project-sponsored by SRF for ROCS, SEM
文摘A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.
基金partially supported by the NationalNatural Science Foundation of China(12171024,11901025,11971217,11971020)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027)。
文摘This paper is concerned with a diffuse interface model called Navier-Stokes/CahnHilliard system.This model is usually used to describe the motion of immiscible two-phase flows with a diffusion interface.For the periodic boundary value problem of this system in torus T3,we prove that there exists a global unique strong solution near the phase separation state,which means that no vacuum,shock wave,mass concentration,interface collision or rupture will be developed in finite time.Furthermore,we establish the large time behavior of the global strong solution of this system.In particular,we find that the phase field decays algebraically to the phase separation state.
基金partially supported by the key research project of National Natural Science Foundation of China (Grant No.11931010)。
文摘In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of Schonbek and the spectrum analysis method, and for the high frequency part, we use the global energy estimate and the behavior of exponentially decay operator.
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].
基金A The research is supported in part by the National Natural Science Foundation of China （Grant No. 10401012） and The Project Sponsored by the Scientific Research Foundation for the Returned 0verseas Chinese Scholars, State Education Ministry.Acknowledgment This is a part of my Ph.D thesis at The Institute of Mathematical Sciences, The Chinese University of Hong Kong. I express my deep gratitude to my graduate advisor, Professor Zhouping Xin, for his guidance and encouragement.
文摘In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows.
文摘Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is proved that the solutions of (1) tend to those of the following nonlinear parabolic equation time-asymptotically:
基金supported by National Natural Science Foundation of China (Grant No.10971171)
文摘Abstract In this paper, we study the stability of solutions of the Cauchy problem for 1-D compressible Narvier- Stokes equations with general initial data. The asymptotic limit of solution is found, under some conditions. The results in this paper imply the case that the limit function of solution as t → ee is a viscous contact wave in the sense, which approximates the contact discontinuity on any finite-time interval as the heat conduction coefficients toward zero. As a by-product, the decay rates of the solution for the fast diffusion equations are also obtained. The proofs are based on the elementary energy method and the study of asymptotic behavior of the solution to the fast diffusion equation.
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 the Collaborative Innovation Center on Beijing Society-building and Social GovernanceNSFC(11371042)+2 种基金BNSF(1132006)the key fund of the Beijing education committee of ChinaChina Postdoctoral Science Foundation funded project
文摘This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ｜｜·｜｜H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ｜｜·｜｜H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.
文摘The purpose of this paper is t0 investigate an irreversible model in the kine-tics of heterogeneous cataIytic reaction-diffusion. The existence, uniqueness andlarge-time behavior of solutions are proved. Particularly, the result shows thatthe reaction ceare in nnite time provided there is some kinds of absorption.
基金the MST Grant #1999075107 and the Innovation funds of AMSS, CAS of China.
文摘The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered respectively. The global existence of smooth solutions to the IBVP problems for two systems are proved, and their large-time behavior is analyzed. The time-asymptotic equivalence of these two systems are investigated, the decay rate of the difference of solutions between these two systems are shown to be determined explicitly by the initial perturbations and boundary effects. It is found that the oscillation of the specific volume can be cancelled by that of entropy, i.e., the oscillation of the specific volume and entropy is not required to be small.
基金supported by National Natural Science Foundation of China(Grant Nos.11801223 and 11871267)supported by National Natural Science Foundation of China(Grant No.11501437)+2 种基金supported by National Natural Science Foundation of China(Grant Nos.11631006 and 11790272)the China Post-doctoral Science Foundation(Grant No.2017M611439)Shanghai Science and Technology Commission(Grant No.17XD1400500)。
文摘In this paper,we investigate the non-autonomous Hamilton-Jacobi equation{ə_(t)u+H(t,x,ə_(x)=0,u(x,t)_(0))=φ(x),x∈M where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_(0))^(t)φ(x)and show T_(t_(0))^(t)φ(x)converges uniformly to a time-periodic viscosity solution u^(*)(x,t)ofə_(t)u+H(t,x,ə_(x)u,u)=0.
