Sonic-supersonic solutions for the two dimensional steady relativistic Euler equations

Abstract

In this paper, we study the existence of the sonic-supersonic solution for the 2D steady isentropic relativistic Euler equations. Employing the characteristic decomposition of two dependent variables, 2D relativistic Euler equations are transformed into the first-order hyperbolic equations. Based on the first-order hyperbolic equations and the transformation (q2−a2,Φ) introduced by Zhang and Zheng (2014), we transform the problem into a homogeneous boundary value problem. Utilizing the method of iteration, the existence of the classical solution is proved in (t,Φ) plane. Moreover, the sonic-supersonic solution is verified in (x,y) plane. Finally, we give the C1,16 regularity of sonic-supersonic solution near the sonic curve.