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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:437

Article

Fang, Beixiang^1,2  Xiang, Wei³ 

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China

[3] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

关键词: Uniqueness;    Transonic shocks;    2-D wedge;    Potential flow equation;   

DOI  :  10.1016/j.jmaa.2015.11.067

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free