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Abstract
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As indicated in Section 111 of Courant and Friedrichs's book [Supersonic Flow and Shock Waves, Interscience, New York, 1948], a supersonic flow around a bend, one of the most important elementary flows, is effected by a rarefaction wave. This paper is concerned with the local structural stability of a multidimensional complete rarefaction wave for the 3-D steady supersonic flow past a large bend. More concretely, by taking the involved analysis on the resulting degenerate hyperbolic equation near the vacuum boundary
and establishing the related energy estimates with suitable degenerate weights, we prove the local existence and stability of a multidimensional complete expansion wave including a vacuum boundary when a perturbed supersonic incoming flow moves around the large bend. This is a joint work with Prof.Yin Huicheng and Dr.Zhu Lu.
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