PRANDTL-MEYER REFLECTION FOR SUPERSONIC FLOW PAST A SOLID RAMP

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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.
Publisher
BROWN UNIV
Issue Date
2013
Language
English
Article Type
Article
Citation

QUARTERLY OF APPLIED MATHEMATICS, v.71, no.3, pp.583 - 600

ISSN
0033-569X
DOI
10.1090/S0033-569X-2013-01335-2
URI
http://hdl.handle.net/10203/280622
Appears in Collection
MA-Journal Papers(저널논문)
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