Energy Conservation For The Weak Solutions Of Three-dimensional Compressible MHD Equations

In this paper,we mainly prove the energy conservation for the weak solutions of the three-dimensional compressible MHD equations in a bounded domain with periodic boundary conditions.The analysis is based on the method of the energy conservation of compressible Navier-Stokes equations.However compared with the Navier-Stokes equa-tions,the MHD equation has more magnetic fields,which makes the problem more com-plicated.Therefore,in this paper,we mainly focus on the processing of the magnetic field term.It should be pointed out that although the magnetic field is present,in order to make the energy equation of the weak solution hold in the result of the theorem,We only add the L_t~p-L_x~qregularity conditions to the velocity field u without adding a regularity condition to the magnetic field term.This paper is divided into three chapters:The first chapter,which summarizes the background,significance of the research and research progress.Briefly describes the main work of this study and the difficulties encountered in the process of proof.The second chapter,We briefly introduce the symbols,notations,and the lemmas and inequalities needed in the proof process.The third chapter,prove the main theorem.