Global Existence And Optimal Decay Rate Of Solutions For Bipolar Compressible Navier - Stokes - Poisson Equation With External Force

In this paper, we consider the three dimensional compressible bipolar Navier-Stokes-Poissonequations with the potential external force. Under the smallness assumption of the external force insome Sobolev space, the existence of the stationary solution is established by solving a nonlinearcoupled elliptic system. Next, we show global well-posedness of the initial value problem for thethree dimensional compressible bipolar Navier-Stokes-Poisson equations, provided the prescirbedinitial date is close to the stationary solution. Finally, based on the elaborate energy estimates forthe nonlinear system and L2-decay estimates for semigroup generated by the lineairzed equation,we give the optimal L2-convergence rates of the solutions towards the stationary solution.This paper is organized as follows.Chapter One is an introduction. It is devoted to introducing physical background and previousmathematical research works on shock relfection and diffraction. The main problems, main resultsin this dissertation are also illustrated.In Chapter Two, we present the unique existence of the stationary solution for the compress?ible isentropic bipolar Navier-Stokes-Poisson equations. The global existence of smooth solutionsfor this problem is proved in Chapter Three. In Chapter Four, we establish the optimal L2timedecay rates of smoolh solutions constructed in Chapter Three.In Chapter Five，we present the unique existence of the stationary solution for the compress?ible non-i sen tropic bipolar Navier-Stokes-Poisson equations. The global existence of smooth so?lutions for this problem is proved in Chapter Six. In Chapter Seven, we establish the optimal L2time decay rates of smooth solutions constructed in Chapter Six.