The Expansion Of A Non-ideal Gas Around A Sharp Corner For 2-D Compressible Euler System

Nonlinear hyperbolic conservation law equations is an important branch in the research field of partial differential equations,and its application involves much natural phenomena.It plays a vital role in many important disciplines.This system can be used to describe and solve a kind of problems related to real life.We describe our research in the following sections.In chapter 1,the research status related to the flow diffusion problem is expounded and the main work we have done is briefly explainedIn chapter 2,we introduce some basic knowledge to understand the work in this paper,such as fluid mechanics equations,some basic flow types such as steady flow and isentropic flow,and two kinds of gas state equations.In chapter 3,we establish a two-dimensional self-similar steady flow of fluid mechanics equations with initial boundary conditions,and make corresponding characteristic analysis,including characteristic direction and pseudo-flow direction.Then we derive characteristic equations related to variables α,β and c,and the characteristic decomposition of variable c on the self-similar plane.We will use these relations to establish the hyperbolic nature of subsequent estimation and solution.In chapter 4,we first introduce the definition of central sparse wave,and construct a two-dimensional self-similar central simple wave for constant compressible flow.Secondly,we consider the two-dimensional Riemann problem of fluid mechanics equations with initial values and discuss the interaction between central sparse wave and plane sparse wave.Finally,it is concluded that the related problems can be reduced to the standard Goursant problem.Thus,the existence of solutions is obtained by generalization.