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May/June 2020 On a global supersonic-sonic patch characterized by 2-D steady full Euler equations
Yanbo Hu, Jiequan Li
Adv. Differential Equations 25(5/6): 213-254 (May/June 2020).

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 $C^{1,\frac{1}{6}}$ continuous up to the sonic curve and the sonic curve is also $C^{1,\frac{1}{6}}$ continuous.

Citation

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Yanbo Hu. Jiequan Li. "On a global supersonic-sonic patch characterized by 2-D steady full Euler equations." Adv. Differential Equations 25 (5/6) 213 - 254, May/June 2020.

Information

Published: May/June 2020
First available in Project Euclid: 16 May 2020

zbMATH: 07243143
MathSciNet: MR4099219

Subjects:
Primary: 35L65, 35L80, 76H05

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.25 • No. 5/6 • May/June 2020
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