Stability Of Linearized System For The Bipolar Compressible Navier-Stokes-Maxwell System

In this paper,the fluid dynamics model describing electrons and ions under the influence of self-consistent electromagnetic field in Plasma Physics is researched,and the Cauchy problem on the bipolar compressible Navier-Stokes-Maxwell equations is studied.In the three-dimensional case,the global existence of the smooth solutions of the system has been solved,therefore this paper focuses on the time decay rates of the global solutions for linearized system.Using the decay structure of the Navier-Stokes-Maxwell equations,we first separate the bipolar system and obtain two coupled subsystems.Based on the linearized analysis of the unipolar Navier-Stokes-Maxwell system and the damped Navier-Stokes system,we can accurately obtain the time decay rates of the global smooth solutions for linearized system.The structure of this paper is arranged as follows:In Chapter 1,the research background and significance of the model are intro-duced,and the bipolar compressible Navier-Stokes-Maxwell system studied in this pa-per is explained,where the research status of the model at home and abroad also be described in detail.Finally,the main research conclusions of this paper are given.In Chapter 2,the mathematical notations and the related preliminary knowledge used in this paper are given.In Chapter 3,the explicit representation and time decay property of solutions for linearized homogeneous system are studied.First,two linearized systems are obtained by differentiating the nonlinear Navier-Stokes-Maxwell system.Secondly,based on the theory of ODE and Fourier analysis,the explicit representation of solutions of Cauchy problem for linearized homogeneous system is determined.Finally,using the Hausdorff-Young inequality,the refined time decay property of solutions is obtained.