On the existence and regularity of solutions of semihyperbolic patches to 2‐D Euler equations with van der Waals gas

Abstract

AbstractThis article is concerned in establishing the existence and regularity of solution of semihyperbolic patch problem for two‐dimensional isentropic Euler equations with van der Waals gas. This type of solution appears in the transonic flow over an airfoil and Guderley reflection and is very common in the numerical solution of Riemann problems. We use the idea of characteristic decomposition and bootstrap method to prove the existence of a global smooth solution, which is uniformly continuous up to the sonic curve. We also prove that the sonic curve is continuous. Further, we show the formation of shock as an envelope for positive characteristics before reaching their sonic points.