Consider compressible fluid flow onto a solid wedge, symmetric in the flow direction (see Fig. 1). It is known from experiments and numerics that for supersonic flow, the time-asymptotic (steady) state consists of one straight shock on each side, emanating downstream. Each shock separates two constant-state regions, the upstream, and downstream area. The downstream area has higher density, but lower velocity, with direction tangential to the wedge surface. An alternative point of view is to consider flow parallel to a wall, up to a concave corner.
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References
Gui-Qiang Chen and M. Feldman, Global solutions to shock reflection by large-angle wedges for potential flow, Annals of Math. (to appear).
V. Elling and Tai-Ping Liu, The ellipticity principle for selfsimilar potential flow, J. Hyper. Diff. Eqns. 2 (2005), no. 4, 909–917, See also arxiv:math.AP-0509332.
G. Lieberman, Hölder continuity of the gradient at a corner for the capillary problem and related results, Pac. J. Math. 133 (1988), no. 1, 115–135.
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Elling, V., Liu, T.P. (2008). Exact Solutions to Supersonic Flow onto a Solid Wedge. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_8
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