Global Existence Of Strong Solutions For One-Dimensional Compressible Navier-Stokes Equations With Thermal Radiation And Degenerate Heat Conduction

In this paper,we study the initial boundary value problem of compressible onedimensional Navier Stokes equations under external pressure boundary conditions.In particular,under the action of high temperature,we study the motion law of viscous radiation reactive gases.Under the assumption that the viscosity coefficient is constant and the thermal conductivity coefficient is a power function of temperature,we study the global existence of strong solutions for initial boundary value problems with large initial values.The key to solving this initial boundary value problem is to obtain positive upper and lower bounds on density and temperature.The main research content is as follows:In Chapter 1,this article mainly describes the research background,purpose,and significance of one-dimensional compressible Navier Stokes equations.It describes the research progress and current status of one-dimensional compressible Navier Stokes equations at home and abroad,and introduces some important achievements obtained by domestic and foreign researchers on compressible viscous gases.Chapter 2 mainly describes some basic function spaces,basic inequalities,basic lemmas,and important conclusions mentioned and applied in this article.Chapter 3 provides a detailed description of the results of this study and its proof process,proving the global existence and uniqueness of strong solutions for compressible one-dimensional Navier Stokes equations with thermal radiation and degenerate heat conduction.In this paper,we assume that the viscosity coefficient is a constant and the heat conductivity coefficient is a power function of temperature.Through the basic energy estimation,we find that both density and temperature have positive upper and lower bounds,thus proving the global existence of strong solutions to the initial boundary value problem(1.1)-(1.7)with large initial values.Chapter 4 mainly summarizes the processing process of the research results in this article and proposes topics that may require further research in the future.