2011/12/31 by Myoungjean Bae, Gui‐Qiang Chen, Gui-Qiang Chen +4 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #35B65 #35J67 #35J70 #35L15 #35L20 #35L65 #35L67 #35L70 #35M10 #35M12 #35R35 #76H05 #76L05 #76N10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #J.2 #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #acm:35B65 #acm:35J67 #acm:35J70 #acm:35L15 #acm:35L20 #acm:35L65 #acm:35L67 #acm:35L70 #acm:35M10 #acm:35M12 #acm:35R35 #acm:76H05 #acm:76L05 #acm:76N10 #math-ph #math.AP #math.MP #msc:35B65 #msc:35J67 #msc:35J70 #msc:35L15 #msc:35L20 #msc:35L65 #msc:35L67 #msc:35L70 #msc:35M10 #msc:35M12 #msc:35R35 #msc:76H05 #msc:76L05 #msc:76N10
paper · pdf · doi:10.48550/arxiv.1201.0294
19 pages, 5 figures
arxiv created 2011/12/31 · openalex publication_date 2011/12/31 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 asymptotics 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 apriori estimates for weak solutions, which allow us to employ the Leray-Schauder degree argument to complete the theory for the general case.