On a global supersonic-sonic patch characterized by 2-D steady full Euler equations

2019/04/10 by Yanbo Hu, Hu, Yanbo, Jiequan Li +1
Engineering · Mathematics · #35L65 #35L80 #76H05 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1904.05479

openalex publication_date 2019/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Supersonic-sonic patches are ubiquitous in regions of transonic flows and they boil down to a family of degenerate hyperbolic problems in regions surrounded by a streamline, a characteristic curve and a possible sonic curve. This paper establishes the global existence of solutions in a whole supersonic-sonic patch characterized by the two-dimensional full system of steady Euler equations and studies solution behaviors near sonic curves, depending on the proper choice of boundary data extracted from the airfoil problem and related contexts. New characteristic decompositions are developed for the full system and a delicate local partial hodograph transformation is introduced for the solution estimates. It is shown that the solution is uniformly C^1,(1)/(6) continuous up to the sonic curve and the sonic curve is also C^1,(1)/(6) continuous.

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