Advances in Differential Equations

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

Yanbo Hu and Jiequan Li

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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.

Article information

Adv. Differential Equations, Volume 25, Number 5/6 (2020), 213-254.

First available in Project Euclid: 16 May 2020

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Primary: 35L65: Conservation laws 35L80: Degenerate hyperbolic equations 76H05: Transonic flows


Hu, Yanbo; Li, Jiequan. On a global supersonic-sonic patch characterized by 2-D steady full Euler equations. Adv. Differential Equations 25 (2020), no. 5/6, 213--254.

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