Solutions of the Ultra-Relativistic Euler Equations in Riemann InvariantsAbdelrahman MAE* and Moaaz O
Department of Mathematics, Faculty of Science, Mansoura University, Egypt
- *Corresponding Author:
- Abdelrahman MAE
Professor, Department of Mathematics
Faculty of Science, Mansoura University, Egypt
E-mail: [email protected]
Received Date: March 06, 2017; Accepted Date: April 25, 2017; Published Date: April 28, 2017
Citation: Abdelrahman MAE, Moaaz O (2017) Solutions of the Ultra-Relativistic Euler Equations in Riemann Invariants. J Phys Math 8: 222. doi: 10.4172/2090-0902.1000222
Copyright: © 2017 Abdelrahman MAE, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In this paper we introduce a new technique for constructing solutions of the ultra-relativistic Euler equations. The Riemann invariants are formulated. We also give some applications of the Riemann invariants. We firstly study the geometric properties of the solution in Riemann invariants coordinates. The other application of Riemann invariants, representing the ultra-relativistic Euler equations in diagonal form, which admits the existence of global smooth solution for the ultra-relativistic Euler equations.