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 bipolar compressible Euler-Maxwell equations as a fluid dynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions is investigated. This work is concerned with three-...The bipolar compressible Euler-Maxwell equations as a fluid dynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions is investigated. This work is concerned with three-dimensional Euler-Maxwell equations with smooth periodic solutions. With the help of the symmetry operator techniques and energy method, the global smooth solution with small amplitude is constructed around a constant equilibrium solution with asymptotic stability property.展开更多
In this paper,we study the regularity of solutions of nonlinear stochastic partial differential equations(SPDEs)with multiplicative noises in the framework of Hilbert scales.Then we apply our abstract result to severa...In this paper,we study the regularity of solutions of nonlinear stochastic partial differential equations(SPDEs)with multiplicative noises in the framework of Hilbert scales.Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line,stochastic 2D Navier-Stokes equations(SNSEs)in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space,and obtain the existence of their smooth solutions respectively.In particular,we also get the existence of local smooth solutions for 3D SNSEs.展开更多
In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases.Under the assumption that the initial data is close to a constant state and the vorticity of the initial vel...In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases.Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes,we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.展开更多
The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the syst...The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the system and applying the FriedrichsLax-Kato theory of symmetric hyperbolic systems.For the non-vacuum case,according to Godunov,firstly a strictly convex entropy function is solved out,then a suitable symmetrizer to symmetrize the system is constructed.For the vacuum case,since the coefficient matrix blows-up near the vacuum,the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.展开更多
Under the assumptions that the initial density ρ0 is close enough to 1 and ρ0-1∈Hs+1(R2);u0∈Hs(R2)∩H_∈(R2) for s>2 and 0<ε<1;the authors prove the global existence and uniqueness of smooth solutions to...Under the assumptions that the initial density ρ0 is close enough to 1 and ρ0-1∈Hs+1(R2);u0∈Hs(R2)∩H_∈(R2) for s>2 and 0<ε<1;the authors prove the global existence and uniqueness of smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid.Furthermore,the L2 decay rate of the velocity field is obtained.展开更多
We show the blow-up of smooth solutions to a non-isothermal model of capillary compressible fluids in arbitrary space dimensions with initial density of compact support. This is an extension of Xin＇s result [Xin, Z....We show the blow-up of smooth solutions to a non-isothermal model of capillary compressible fluids in arbitrary space dimensions with initial density of compact support. This is an extension of Xin＇s result [Xin, Z.： Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density. Comm. Pure Appl. Math., 51, 229-240 （1998）] to the capillary case but we do not need the condition that the entropy is bounded below. Moreover, from the proof of Theorem 1.2, we also obtain the exact relationship between the size of support of the initial density and the life span of the solutions. We also present a sufficient condition on the blow-up of smooth solutions to the compressible fluid models of Korteweg type when the initial density is positive but has a decay at infinity.展开更多
We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work.The diffusion of mixed partial viscosity is weaker than that of fu...We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work.The diffusion of mixed partial viscosity is weaker than that of full viscosity,which cases new difficulty in proving global smooth solutions.Moreover,Hall term heightens the level of nonlinearity of the standard MHD system.Global smooth solutions are established by using energy method and the bootstrapping argument,provided that the initial data is enough small.展开更多
The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem...The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem. First, it is proved that the solutions to these two systems converge to the unique stationary solution time asymptotically without the smallness assump- tion on doping profile. Then, very sharp estimates on the smooth solutions, independent of the relaxation time, are obtained and used to establish the zero relaxation limit.展开更多
In this article, we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise. We prove the existence and uniqueness of smooth solutions to this equation with difference method.
In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotationa...In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotational degeneracy of hyperbolic systems of conservation laws(Ⅱ).sufficient conditions which guarantee the existence of gloats smooth solutions of the Cauchy problems (Ⅰ) and (Ⅱ) are obtained by employing the characteristic method.展开更多
Considering the Navier-Stokes-Landau-Lifshitz-Maxwell equations,in dimensions two and three,we use Galerkin method to prove the existence of weak solution.Then combine the a priori estimates and induction technique,we...Considering the Navier-Stokes-Landau-Lifshitz-Maxwell equations,in dimensions two and three,we use Galerkin method to prove the existence of weak solution.Then combine the a priori estimates and induction technique,we obtain the existence of smooth solution.展开更多
Concerning the development trend of the GSM/GPRS network,and from the angle of radio networks and core networks,this article pre- sents three concrete solutions to the evolution towards WCDMA.It points out that the ov...Concerning the development trend of the GSM/GPRS network,and from the angle of radio networks and core networks,this article pre- sents three concrete solutions to the evolution towards WCDMA.It points out that the overlay network scheme has the minimum impact on the operation of current networks,and ensures the evolution of NGN to all-IP networks and the smooth transition of 2G services.展开更多
In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equat...In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.展开更多
We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋...We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋1 of first category, defined in the range of the initial datum.展开更多
In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbati...In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.展开更多
We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSS...We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.展开更多
In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then...In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then by combining some a priori estimates,continuity argument,the local smooth solution is extended step by step to all t>0 provided that the L1 norm of initial data is suitably small and the smooth nonlinear functions f(u)and g(u)satisfy certain local growth conditions at some fixed point■.展开更多
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.
基金Supported by the Foundation Project of Doctor Graduate Student Innovation of Beijing University of Technology(ykj-2012-6724)Supported by the NSFC(10771009)Supported by the BSF(1082001)
文摘The bipolar compressible Euler-Maxwell equations as a fluid dynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions is investigated. This work is concerned with three-dimensional Euler-Maxwell equations with smooth periodic solutions. With the help of the symmetry operator techniques and energy method, the global smooth solution with small amplitude is constructed around a constant equilibrium solution with asymptotic stability property.
基金supported by National Natural Science Foundation of China (Grant Nos. 10971076, 10871215)
文摘In this paper,we study the regularity of solutions of nonlinear stochastic partial differential equations(SPDEs)with multiplicative noises in the framework of Hilbert scales.Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line,stochastic 2D Navier-Stokes equations(SNSEs)in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space,and obtain the existence of their smooth solutions respectively.In particular,we also get the existence of local smooth solutions for 3D SNSEs.
基金supported by National Natural Science Foundation of China(Grant No.10671124)
文摘In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases.Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes,we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.
基金supported by the National Natural Science Foundation of China(Nos.11201308,10971135)the Science Foundation for the Excellent Youth Scholars of Shanghai Municipal Education Commission(No.ZZyyy12025)+1 种基金the Innovation Program of Shanghai Municipal Education Commission(No.13zz136)the Science Foundation of Yin Jin Ren Cai of Shanghai Institute of Technology(No.YJ2011-03)
文摘The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the system and applying the FriedrichsLax-Kato theory of symmetric hyperbolic systems.For the non-vacuum case,according to Godunov,firstly a strictly convex entropy function is solved out,then a suitable symmetrizer to symmetrize the system is constructed.For the vacuum case,since the coefficient matrix blows-up near the vacuum,the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.
基金Project supported by the National Natural Science Foundation of China (Nos.10525101,10421101)the 973 project of the Ministry of Science and Technology of Chinathe innovation grant from Chinese Academy of Sciences
文摘Under the assumptions that the initial density ρ0 is close enough to 1 and ρ0-1∈Hs+1(R2);u0∈Hs(R2)∩H_∈(R2) for s>2 and 0<ε<1;the authors prove the global existence and uniqueness of smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid.Furthermore,the L2 decay rate of the velocity field is obtained.
基金Supported by National Natural Science Foundation of China-NSAF (Grant No. 10976026)
文摘We show the blow-up of smooth solutions to a non-isothermal model of capillary compressible fluids in arbitrary space dimensions with initial density of compact support. This is an extension of Xin＇s result [Xin, Z.： Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density. Comm. Pure Appl. Math., 51, 229-240 （1998）] to the capillary case but we do not need the condition that the entropy is bounded below. Moreover, from the proof of Theorem 1.2, we also obtain the exact relationship between the size of support of the initial density and the life span of the solutions. We also present a sufficient condition on the blow-up of smooth solutions to the compressible fluid models of Korteweg type when the initial density is positive but has a decay at infinity.
基金supported by the NNSF of China(Grant No.11871212)Basic Research Project of Key Scientific Research Project Plan of Universities in Henan Province(No.20ZX002).
文摘We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work.The diffusion of mixed partial viscosity is weaker than that of full viscosity,which cases new difficulty in proving global smooth solutions.Moreover,Hall term heightens the level of nonlinearity of the standard MHD system.Global smooth solutions are established by using energy method and the bootstrapping argument,provided that the initial data is enough small.
基金Project supported by the National Natural Science Foundation of China, the Grant of MST of China,the National Natural Science
文摘The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem. First, it is proved that the solutions to these two systems converge to the unique stationary solution time asymptotically without the smallness assump- tion on doping profile. Then, very sharp estimates on the smooth solutions, independent of the relaxation time, are obtained and used to establish the zero relaxation limit.
基金The first author is supported by National Natural Science Foundation of China （Grant No. 11001285） The authors thank the referees for their careful reading and helpful suggestions and comments, which improve the original manuscript greatly.
文摘In this article, we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise. We prove the existence and uniqueness of smooth solutions to this equation with difference method.
文摘In this paper,we study the global smooth solutions of the Cauchy problem for two important nonstrictly quasilinear hyperbolic systems.i.e.,the isentropic gas dynamics system in Euler coordinates (Ⅰ) and the rotational degeneracy of hyperbolic systems of conservation laws(Ⅱ).sufficient conditions which guarantee the existence of gloats smooth solutions of the Cauchy problems (Ⅰ) and (Ⅱ) are obtained by employing the characteristic method.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11731014,11571254).
文摘Considering the Navier-Stokes-Landau-Lifshitz-Maxwell equations,in dimensions two and three,we use Galerkin method to prove the existence of weak solution.Then combine the a priori estimates and induction technique,we obtain the existence of smooth solution.
文摘Concerning the development trend of the GSM/GPRS network,and from the angle of radio networks and core networks,this article pre- sents three concrete solutions to the evolution towards WCDMA.It points out that the overlay network scheme has the minimum impact on the operation of current networks,and ensures the evolution of NGN to all-IP networks and the smooth transition of 2G services.
基金the Youngth Program of Hubei Provincial Department of Education (Q200628002)the Innovation Program of Shanghai Municipal Education Commission (08YZ72)
文摘In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.
基金supported by National Natural Foundation of China(10671116 and 10871133)
文摘We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k＋1 of first category, defined in the range of the initial datum.
基金NUAA's Scientific Fund for the Introduction of Qualified Personnel and the National Natural Science Foundation of China(10571158).
文摘In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.
文摘We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.N2005031)。
文摘In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then by combining some a priori estimates,continuity argument,the local smooth solution is extended step by step to all t>0 provided that the L1 norm of initial data is suitably small and the smooth nonlinear functions f(u)and g(u)satisfy certain local growth conditions at some fixed point■.
