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PRANDTL-MEYER REFLECTION FOR SUPERSONIC FLOW PAST A SOLID RAMP SCIE SCOPUS

Title
PRANDTL-MEYER REFLECTION FOR SUPERSONIC FLOW PAST A SOLID RAMP
Authors
Bae, MGui-Qiang G. ChenMikhail Feldman
Date Issued
2013-09
Publisher
AMS
Abstract
We present our recent results on the Prandtl-Meyer reflection for supersonic potential flow past a solid ramp. When a steady supersonic flow passes a solid ramp, there are two possible configurations: the weak shock solution and the strong shock solution. Elling-Liu's theorem (2008) indicates that the steady supersonic weak shock solution can be regarded as a long-time asymptotic state of an unsteady flow for a class of physical parameters determined by certain assumptions for potential flow. In this paper we discuss our recent progress in removing these assumptions and establishing the stability theorem for steady supersonic weak shock solutions as the long-time asymptotics of unsteady flows for all the physical parameters for potential flow. We apply new mathematical techniques developed in our recent work to obtain monotonicity properties and uniform a priori estimates for weak solutions, which allow us to employ the Leray-Schauder degree argument to complete the theory for the general case.
Keywords
randtl-Meyer reflection; supersonic flow; unsteady flow; steady flow; solid wedge; weak shock solution; strong shock solution; stability; self-similar; transonic shock; sonic boundary; free boundary; existence; regularity; elliptic-hyperbolic mixed; monotonicity; apriori estimates; uniform estimates; separation estimates; SHOCK REFLECTION; WEDGE; EXISTENCE; STABILITY
URI
https://oasis.postech.ac.kr/handle/2014.oak/13099
DOI
10.1090/S0033-569X-2013-01335-2
ISSN
0033-569X
Article Type
Article
Citation
QUARTERLY OF APPLIED MATHEMATICS, vol. 71, no. 3, page. 583 - 600, 2013-09
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배명진BAE, MYOUNGJEAN
Dept of Mathematics
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