Hypersonic limit of two‐dimensional steady compressible Euler flows passing a straight wedge
Aifang Qu, Hairong Yuan, Qin Zhao
Abstract
Abstract We formulate a problem on hypersonic limit of two‐dimensional steady non‐isentropic compressible Euler flows passing a straight wedge. It turns out that the Mach number of the upcoming uniform supersonic flow increases to infinity may be taken as that the adiabatic exponent γ of the polytropic gas decreases to 1. We propose a form of the Euler equations which is valid if the unknowns are Radon measures and construct a measure solution containing Dirac measures supported on the surface of the wedge. It is proved that as , the sequence of solutions of the compressible Euler equations that contains a shock ahead of the wedge converges vaguely as measures to the measure solution constructed. This justifies the Newton theory of hypersonic flow passing obstacles in the case of two‐dimensional straight wedges. The result also demonstrates the necessity of considering general measure solutions in the study of boundary‐value problems of systems of hyperbolic conservation laws.