Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

3 Scopus Citations
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Original languageEnglish
Pages (from-to)111–138
Number of pages28
Journal / PublicationCommunications in Mathematical Physics
Volume387
Issue number1
Online published6 Aug 2021
Publication statusPublished - Oct 2021

Abstract

We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the perturbations are away from the wedge edge in the previous results is removed. One of the key ingredients is to identify a good direction of the boundary operator of a boundary condition of the shock along the wedge edge, based on the non-obliqueness of the boundary condition for the weak shock on the edge. With the identification of this direction, an additional boundary condition on the wedge edge can be assigned to make sure that the shock is attached on the edge and linearly stable under small perturbations. Based on the linear stability, we introduce an iteration scheme and prove that there exists a unique fixed point of the iteration scheme, which leads to the global existence and nonlinear structural stability of the attached weak transonic shock. This approach is based on neither the hodograph transformation nor the spectrum analysis, and should be useful for other problems with similar difficulties.