The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations ...The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.展开更多
In this paper, the convergence compressible Euler-Poisson equations in a of time-dependent Euler-Maxwell equations to torus via the non-relativistic limit is studied. The local existence of smooth solutions to both sy...In this paper, the convergence compressible Euler-Poisson equations in a of time-dependent Euler-Maxwell equations to torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy estimates for first order symmetrizable hyperbolic systems. For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order. The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.展开更多
基金supported by the National Natural Science Foundation of China (No. 10671120)the ShanghaiLeading Academic Discipline Project (No. J50101).
文摘The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.
基金Project supported by the European project"Hyperbolic and Kinetic Equations"(No.HPRN-CT-2002-00282)the Natioual Natural Science Foundation of China(No.10471009)the Beijing Science Foundation of China(No.1052001).
文摘In this paper, the convergence compressible Euler-Poisson equations in a of time-dependent Euler-Maxwell equations to torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy estimates for first order symmetrizable hyperbolic systems. For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order. The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.
