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We formulated a problem on hypersonic limit of two-dimensional steadynon-isentropic compressible Euler flows passing a straight wedge. It turns outthat Mach number of the upcoming uniform supersonic flow increases to infinitemay be taken as the adiabatic exponent $\gamma$ of the polytropic gas decreasesto $1$. We proposed a form of the Euler equations which is valid if theunknowns are measures and constructed a measure solution contains Diracmeasures supported on the surface of the wedge. It is proved that as $\gamma\to1$, the sequence of solutions of the compressible Euler equations thatcontaining a shock ahead of the wedge converge vaguely as measures to themeasure solution we constructed. This justified the Newton theory of hypersonicflow passing obstacles in the case of two-dimensional straight wedges. Theresult also demonstrates the necessity of considering general measure solutionsin the studies of boundary-value problems of systems of hyperbolic conservationlaws.

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