Sonic-supersonic solutions to a degenerate Cauchy-Goursat problem for 2D relativistic Euler equations.(English)Zbl 07461638

Summary: In this paper, we consider the degenerate Cauchy-Goursat problem for 2D steady isentropic relativistic Euler equations. Prescribing the sonic curve and a positive characteristic curve as boundaries, the existence and uniqueness of sonic-supersonic solution in an angular region are obtained. Employing the characteristic decomposition of angle variables, 2D relativistic Euler equations are transformed into the first-order hyperbolic equations. In the partial hodograph plane, introducing the change variables $$\overline{W}=\frac{1}{W},\overline{Z}=\frac{-1}{Z}$$, associated with the iterative method in Li, Hu (2019) yields a linear equations and the existence and uniqueness of the smooth sonic-supersonic solutions are established. Finally, we return the solution in the partial hodograph plane to that in the original physical variables.

MSC:

 35Q31 Euler equations 35L65 Hyperbolic conservation laws 35L67 Shocks and singularities for hyperbolic equations 76N15 Gas dynamics (general theory)
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