Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (4): 841-850.

• Articles • Previous Articles     Next Articles

Steady State Solutions of Relativistic Euler Equations with Spherical Symmetry

 GENG Yong-Cai   

  1. School of Science, Shanghai Institute of Technology, Shanghai 200235
  • Received:2013-02-21 Revised:2014-03-15 Online:2014-08-25 Published:2014-08-25
  • Supported by:

    国家自然科学基金(11201308)、上海市优青项目(ZZyyy12025)和上海市创新项目(13ZZ136)资助

Abstract:

In this paper, for isothermal gas, we will think about the existence of classical (Theorem 1.1) and weak (Theorem 1.2) solutions of steady state relativistic Euler equations with spherical symmetry structure, respectively. Theorem 1.1 shows that, by solving two ordinary differential equations and according to the comparison of Mach number M and 1, we establish the existence of classical solutions. Moreover, Theorem 1.2 shows that, under a C2, αα∈(0,1) steady perturbation of the upstream supersonic flow, we will prove the existence of steady multidimensional transonic shocks (hyperbolic-elliptic shocks) for spherically symmetric relativistic Euler equations.

Key words: Relativistic Euler equations, Spherical symmetry,  Steady state solutions

CLC Number: 

  • 60F15
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