Degenerate Cauchy–Goursat problem for 2‐D steady isentropic Euler system with van der Waals gas

Abstract

This study concerns with the existence–uniqueness of local classical sonic‐supersonic solution to a degenerate Cauchy–Goursat problem that arises in transonic phenomena. The flow is governed by 2‐D steady isentropic Euler system with a polytropic van der Waals gas. The idea of characteristic decomposition has been used to convert the Euler system into a new system involving the angle variables . To overcome the parabolic degeneracy caused at the sonic curve, the partial hodograph transformation and a variety of dependent–independent variables have been introduced to transform the nonlinear system into a linear one with explicit singularity–regularity structure. The uniform convergence of the sequences has been discussed by employing the mathematical induction. Eventually, the inversion of the solution from partial hodograph plane to the original plane has been established.