Uniform Global Existence And Convergence For The Smooth Solutions Of Navier-Stokes-Poisson Equations With Physical Parameters

This paper is concerned with mathematical models arising in plasma physics and semiconductors with two parameters,compressible Navier-Stokes-Poisson(NSP)system in several space dimensions.The systems belong to the class of first-order quasi-linear symmetrizable hyperbolic systems which are partially dissipative.First,the symmetrizable hyperbolic groups are obtained by using the symmetrization method.Then,we using the energy estimates and dissipation estimates methods,which prove that each parameter tends to 0 or both parameters tend to 0,the uniform global existence and convergence of the smooth solution,when the initial value is near the constant equilibrium state.The structure of the present paper is organized as follow:In chapter one,we introduce the research development of NSP systems.Then,we give the main results of this paper.In chapter two,we give some necessary preliminaries of energy estimates of this paper.In chapter three,considering the compressible NSP equations.Firstly,we transform the equations into symmetrizable hyperbolic groups,and then use the energy estimation method to estimate the time dissipation of ?u and N.In chapter four,the proof of the existence and convergence of the global solution of the system.