The Study Of Solutions For The Fluid Equations With Poisson Term

In this paper,we mainly focus on the fluid equations with Poisson term such as Euler-Poisson equations and Navier-Stokes-Poisson equations.Our research covers two aspects in term of every different model,some existence and decay rate results are obtained respectively.In the second chapter,we mainly study the existence and the decay rate of the global solutions of a class of Euler-Poisson equations governing the initial value problem in three space dimensions.In this section,only the solutions in the neighborhood of the constant state are discussed.At first,we obtain new equations by changing the variables.Secondly,we divide the new equations into linear terms and nonlinear terms respectively.Lastly,by means of a series of methods such as the linear analysis,a priori estimates and energy estimates,we obtain the existence and the decay rate of the solutions of the compressible,viscous and heat-conductive fluids.In the third chapter,we mainly study the solutions in the neighborhood of the constant state of a class of Navier-Stokes-Poisson equations governing the initial value problem in three space dimensions.By using the methods mentioned previously,we get the existence of local solutions,a priori estimates and the decay rate of global solutions of the compressible,viscous and heat-conductive fluids.