The Global Existence Of Solutions For Euler Equations Of Mixed Gases

The basic equation of the kinetic theory of gases is first named by Boltzmann in 1872.It is one nonlinear differential equation is used to describe the change of velocity distribution func-tion of gas molecules.Especially in mixed gases The Boltzmann equation and Euler equation are two important equations in gas dynamics.Boltzmann equation and Euler equation are impor-tant research topics.They also attach great importance both at home and abroad.Challenging research topics,these topics all have strong practical background and application significance.Mixed gas in Europe The equations of pull can be deduced by the moment method through the distribution function of gas molecules in Boltzmann equation.This paper studies It is the global existence of the solution of Cauchy problem for the two gas Euler equations in the Lagrange coordinates.Use of the classical typical energy estimation,H¨older inequality technique to get consistent estimates of solutions.It is proved that the mixture of gas is in Europe.The whole existence of the solution of the tension equations.The full text is divided into three chapters.In the first chapter,we introduce the Boltz-mann equation model of N gas and fluid mechanics.The research status of Euler equations and Maxwell-Stefan equations at home and abroad is introduced,and the gas in N is deduced.The Euler equations are given.Finally,the main conclusions of this paper are given.The second chapter is mainly about basic knowledge.The important inequalities that need to be used.The third chapter is a priori estimate.The main content of this chapter is the proof of theorem 1.1.In the first section of this chapter,we first give the low order priori estimates of solutions,and obtain the L~2estimates of solutions by classical energy method.In the second section,we further use the classical energy estimation method to solve the L~2norm estimation for spatial deriva-tives.Thus,the H~3mode estimation of the solution is obtained.The third section is a summary of this chapter.