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
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
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.
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
We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent devel...We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.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
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
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
We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time b...We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously.展开更多
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 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.
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The research of Gui-Qiang G.Chen was supported in part by the UK Engineering and Physical Sciences Research Council Awards EP/L015811/1,EP/V008854/1,EP/V051121/1the Royal Society-Wolfson Research Merit Award WM090014.
文摘We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.
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.
基金Supported by the National Natural Science Foundation of China(No.11071195)partially supported by the National Natural Science Foundation of China(No.11071195)a research grant at the Northwest University
文摘We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously.