Global Existence Of Strong Solutions To Planar Magnetohydrodynamic Equations With Thermal Radiation And Degenerate Heat Conductivity

In this paper,we mainly study the global existence of strong solutions for planar magnetohydrodynamic(MHD)equations with external pressure boundary conditions.In particular,we consider the influence of radiation on fluid dynamics at high temperature.Under the assumption of degenerate heat conduction coefficient and external pressure,based on the local existence and uniqueness of the strong solution of the compressible plane magnetohydrodynamic equation,the local solution of the equation is extended to any time T by using a priori estimation such as energy estimation.Then we prove the global existence and uniqueness of the strong solution of the initial boundary value problem.The key to the problem is to obtain the positive upper and lower bounds of specific volume v and temperature θ.The structure of this paper is as follows :In the first chapter,we will review the fluid dynamics and introduce the plane magnetohydrodynamic equations in four sections,including the research background,research status,preliminary knowledge and main contents.We will introduce the research results of plane magnetohydrodynamic equations by domestic and foreign researchers,and list some basic spaces,concepts,important inequalities and results needed in this paper.In the second chapter,we will study the global existence of strong solutions for the planar MHD equations with thermal radiation and degenerate thermal conductivity.We establish the global existence of strong solutions for the initial-boundary value problem,and prove that the specific volume and temperature have positive upper and lower bounds.In the third chapter,we will summarize the results of this paper,and put forward the problems to be further considered and the direction of future research work.