The uniqueness of transonic shocks in supersonic flow past a 2-D wedge

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Original languageEnglish
Pages (from-to)194-213
Journal / PublicationJournal of Mathematical Analysis and Applications
Issue number1
Online published21 Dec 2015
Publication statusPublished - 1 May 2016


We have proved the uniqueness of transonic shocks in steady supersonic flows past a slightly perturbed two-dimensional infinite wedge, under appropriate conditions on the downstream subsonic flows. We formulate it to a mathematical problem of the uniqueness of solutions of nonlinear partial differential equations of hyperbolic-elliptic mixed type with a free boundary. By working on several elliptic equations of physical quantities separately, we obtain a priori estimates of them, and then prove the uniqueness without assumptions on high regularity. Moreover, uniform estimates on the ellipticity and the positive lower bound of the speed are achieved under a geometrical condition on the wedge. The mathematical ideas and techniques developed here will also be useful for other related problems involving similar analytical difficulties.

Research Area(s)

  • 2-D wedge, Potential flow equation, Transonic shocks, Uniqueness