The Riemann Problem And Boundary Value Problems For The Relativistic Euler Equations

When we consider the fluids movement,the relativistic effects must be considered if the macroscopic velocity of a fluid is close to the speed of light;at the same time,even if the macroscopic velocity of the fluid is not reached the degree of relativistic effect that must be considered,the relativistic effect can not be ignored when the average speed of baryon is close to the speed of light.In this dissertation,we study the Riemann problem and boundary value problems of the relativistic Euler equations with the state equation p = p(?)which is satisfying 0<p'(?)<1 ? p"(?)(p(?)+ ?)+ 2p'(?)(1-p'(?))>0.Firstly,we study the Riemann problem and interaction of elementary waves of the Eu-ler system of conservation laws of energy and momentum in special relativity with general equations of state p = p(?).We obtain the existence of global piecewise smooth solutions of these problems.Secondly,We study several types of boundary value problems,including Goursat problem,mixed initial-boundary value problem,and centered wave problem for the two-dimensional isentropic irrotational steady relativistic Euler system.Global classical so-lutions to these boundary value problems are constructed by the method of characteristic decomposition.Using these results,we also construct a global supersonic relativistic jet flow out of a semi-infinite convex duct into vacuum.