Hypersonic limit of two-dimensional steady compressible Euler flows passing a straight wedge

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 γ → 1, 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.