In this paper, we are going to consider the initial value problem with periodic boundarycondition and the Cauchy problem associated with the system of ferromagnetic chain withthe Gilbert damping term Z_t=-εZ×(Z&...In this paper, we are going to consider the initial value problem with periodic boundarycondition and the Cauchy problem associated with the system of ferromagnetic chain withthe Gilbert damping term Z_t=-εZ×(Z×Z_(zz)+Z×Z_(zz), (ε≥0).The existence of a unique smooth solution is established by using the technique of spatialdifference and crucial a priori estimates of higher-order derivatives in Sobolev spaces.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 ve...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
In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the qu...In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.展开更多
In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the （1 ＋ n）-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyp...In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the （1 ＋ n）-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n =2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem; while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.展开更多
In this paper, we prove some results concerning blow-up of viscous compressible reactive （selfgravitating） flows when the initial density is compactly supported and the other initial value satisfy proper conditions....In this paper, we prove some results concerning blow-up of viscous compressible reactive （selfgravitating） flows when the initial density is compactly supported and the other initial value satisfy proper conditions. It extends the work of Xin and Cho to the case of viscous compressible reactive self-gravitating flows equations. We control the lower bound of second moment by total energy and obtain the precise relationship between the size of the support of initial density and the existence time.展开更多
We study the combination of quasi-neutral limit and viscosity limit of smooth solution for the three-dimensional compressible viscous Navier-Stokes-Poisson-Korteweg equation for plasmas and semiconductors.When the Deb...We study the combination of quasi-neutral limit and viscosity limit of smooth solution for the three-dimensional compressible viscous Navier-Stokes-Poisson-Korteweg equation for plasmas and semiconductors.When the Debye length and viscosity coefficients are sufficiently small,the initial value problem of the model has a unique smooth solution in the time interval where the corresponding incompressible Euler equation has a smooth solution.We also establish a sharp convergence rate of smooth solutions for three-dimensional compressible viscous Navier-Stokes-Poisson-Kortewe equation towards those for the incompressible Euler equation in combining quasi-neutral limit and viscosity limit.Moreover,if the incompressible Euler equation has a global smooth solution,the maximal existence time of three-dimensional compressible Navier-Stokes-Poisson-Korteweg equation tends to infinity as the Debye length and viscosity coefficients goes to zero.展开更多
In this paper, we prove the existence of the global smooth solution to the Cauchy problems for a class of diagonalizable high dimensional quasilinear hyperbolic systems consisted of n-equations.
In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.
In this paper, we are concerned with the existence and uniqueness of global smooth solu- tion for the Robin boundary value problem of Landau Lifshitz equations in one dimension when the boundary value depends on time ...In this paper, we are concerned with the existence and uniqueness of global smooth solu- tion for the Robin boundary value problem of Landau Lifshitz equations in one dimension when the boundary value depends on time t. Yhrthermore, by viscosity vanishing approach, we get the existence and uniqueness of the problem without Gilbert damping term when the boundary value is independent of t.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.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, we are going to consider the initial value problem with periodic boundarycondition and the Cauchy problem associated with the system of ferromagnetic chain withthe Gilbert damping term Z_t=-εZ×(Z×Z_(zz)+Z×Z_(zz), (ε≥0).The existence of a unique smooth solution is established by using the technique of spatialdifference and crucial a priori estimates of higher-order derivatives in Sobolev spaces.
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 Foundation of Guangzhou University (Grant No. 2700050357)National Natural Science Foundation of China (Grant No. 11731014)
文摘In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.
基金Supported by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)
文摘In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the （1 ＋ n）-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n =2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem; while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.
基金Supported by the National Natural Science Foundation of China (No. 10531020,10976062 and 11101044)
文摘In this paper, we prove some results concerning blow-up of viscous compressible reactive （selfgravitating） flows when the initial density is compactly supported and the other initial value satisfy proper conditions. It extends the work of Xin and Cho to the case of viscous compressible reactive self-gravitating flows equations. We control the lower bound of second moment by total energy and obtain the precise relationship between the size of the support of initial density and the existence time.
基金Supported by the Research Grant of Department of Education of Hubei Province(Q20142803)
文摘We study the combination of quasi-neutral limit and viscosity limit of smooth solution for the three-dimensional compressible viscous Navier-Stokes-Poisson-Korteweg equation for plasmas and semiconductors.When the Debye length and viscosity coefficients are sufficiently small,the initial value problem of the model has a unique smooth solution in the time interval where the corresponding incompressible Euler equation has a smooth solution.We also establish a sharp convergence rate of smooth solutions for three-dimensional compressible viscous Navier-Stokes-Poisson-Kortewe equation towards those for the incompressible Euler equation in combining quasi-neutral limit and viscosity limit.Moreover,if the incompressible Euler equation has a global smooth solution,the maximal existence time of three-dimensional compressible Navier-Stokes-Poisson-Korteweg equation tends to infinity as the Debye length and viscosity coefficients goes to zero.
文摘In this paper, we prove the existence of the global smooth solution to the Cauchy problems for a class of diagonalizable high dimensional quasilinear hyperbolic systems consisted of n-equations.
文摘In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.
基金Supported by National Basic Research Program of China (973 Program) (Grant No. 2011CB808002)National Natural Science Foundation of China (Grant Nos. 11071086 and 11128102)the University Special Re-search Foundation for Ph.D. Program (Grant No. 20104407110002)
文摘In this paper, we are concerned with the existence and uniqueness of global smooth solu- tion for the Robin boundary value problem of Landau Lifshitz equations in one dimension when the boundary value depends on time t. Yhrthermore, by viscosity vanishing approach, we get the existence and uniqueness of the problem without Gilbert damping term when the boundary value is independent of t.
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.
