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On the existence and regularity of solutions of semi-hyperbolic patches to 2-D Euler equations with van der Waals gas
This article is concerned in establishing the existence and regularity of
solution of semi-hyperbolic 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 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