The Existence Of The Boundary Layer For The One-dimensional Radiative Euler Equations

The radiative Euler equations are a fundamental system to describe the motion of the compressible gas with the radiative heat transfer phenomena,it's a kind of hyperbolic-elliptic coupled system.At present,mathematics workers are concerned about this hot issue.This paper is devoted to studying the boundary layer for the radiative Euler equations in one-dimensional half space.We will show the unique global-in-time solution exist under some smallness conditions.The first chapter is the introduction.Here,we review the physical background and research history of radiative fluid dynamics equations,and explain the main contents and conclusions to be studied.In chapter 2,the existence region and attenuation properties of boundary layer solution of one-dimensional radiative Euler equations are obtained through calculation and analysis.The first section defines a left state of the boundary layer.The second section describes the detailed calculation process and derivation process to obtain the boundary layer wave.The third section explains the main conclusions.In chapter 3,by introducing the difference between the solution and the smooth sparse wave,the outflow problem is mathematically reformulated and the local existence is expressed.Based on the local existence,the global-in-time existence established with a prior estimate can be obtained.In chapter 4,the priori estimate of global existence is proved by basic energy estimate,first-order energy estimate,second-order energy estimate and perturbation estimate of radiation term w.