A new variation for the relativistic Euler equations

Advances in Difference Equations

article

Abdelrahman, Mahmoud A. E.¹  Alkhidhr, Hanan A.³ 

[1] Department of Mathematics, College of Science, Taibah University;Department of Mathematics, Faculty of Science, Mansoura University;Department of Mathematics, College of Science, Qassim University

关键词: Total variation;    Nonlinear waves;    Riemann solutions;    Wave interaction;    Glimm scheme;   

DOI  :  10.1186/s13662-020-02990-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

【 授权许可】

CC BY