Sonic-supersonic solutions for the two dimensional steady relativistic Euler equations. (October 2022) - Fan, Yongqiang; Guo, Lihui; Hu, Yanbo; You, Shouke
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 ( q 2 − a 2, 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 C 1, 1 6 regularity of sonic-supersonic solution near the sonic curve.