Existence Of Global Weak Solutions To The Incompressible Quasi-static Navier-Stokes-Fourier-Maxwell-Poisson System

In this paper,we study the incompressible quasi-static Navier-Stokes-Fourier-Maxwell-Poisson system on T~3×(0,∞):(?)Where u,p,E,B represent the velocity,pressure,electric and magnetic fields of the fluid,respectively.θandρare temperature and density.μ>0 is the viscosity of the fluid.κ>0 is the thermal conductivity.The system was proposed by Arsenio and Saint-Raymond in[1].In this paper,Galerkin method is used to put forward the approximation problem of the system,the Schauder fixed point theorem is used to solve the approximation problem of the system,and some convergence results are obtained by using Banach-Alaoglu theorem and Aubin-Lions lemma,then the global weak solution of the system is obtained.The structure of this paper is as follows:the first chapter mainly introduces the background and status of the research problem,several important function Spaces used in this paper,and lists the main results of this paper.The second chapter is preparatory knowledge.In chapter 3,the proof of the theorem 2.1.2 is given.