Non-existence of strong regular reflections in self-similar potential flow

2011/04/02 by Volker Elling, Elling, Volker
Mathematics · Physics and Astronomy · #76H05 #76L05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Navier-Stokes equation solutions #math.AP #msc:76H05 #msc:76L05

paper · pdf · doi:10.48550/arxiv.1104.0330

openalex publication_date 2011/04/02 · arxiv created 2012/01/23 · arxiv updated 2012/01/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We consider shock reflection which has a well-known local non-uniqueness: the reflected shock can be either of two choices, called weak and strong. We consider cases where existence of a global solution with weak reflected shock has been proven, for compressible potential flow. If there was a global strong-shock solution as well, then potential flow would be ill-posed. However, we prove non-existence of strong-shock analogues in a natural class of candidates.

Related

• Instability of strong regular reflection and counterexamples to the detachment criterion
• Regular reflection in self-similar potential flow and the sonic criterion
• Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential Flow
• Loss of Regularity of Solutions to Shock Reflection Problems by a Non-symmetric Convex Wedge with Potential Flow Equations
• Global Solutions of Shock Reflection by Large-Angle Wedges for Potential Flow