Well-posedness And Large Time Behaviors Of The Bipolar Non-isentropic Compressible Euler-poisson Equations

This paper mainly focuses on the research of three-dimensional bipolar nonisentropic compressible Euler-Poisson equations which arise from the coupling of Euler equation and Poisson equation.The findings of this research suggest the global well-posedness and large time behavior of this system of equations.Firstly,the existence and uniqueness of global solutions is proved by energy estimation.Secondly,a series of energy estimation and linear decay estimation methods are used to obtain the decay estimation of the solution.This thesis consists of four parts:The first chapter is about a brief introduction of the research background,including findings related to mathematical models.The second chapter is about some common used symbolic conventions,as well as some basic conclusions and important lemmas that will be used in the proof of subsequent chapters.In Chapter 3,when the initial value H3 norm is small,by establishing some a priori estimates and using interpolation techniques,we prove the existence and uniqueness of global solutions of bipolar non isentropic compressible Euler-Poisson equations.Chapter 4 is about the findings of time decay rate of the solution when the doping distribution is small and the initial value belongs to LP(1?P<3/2)space.