The regularity of semihyperbolic patches near sonic lines for the 2-d euler system in gas dynamics

Kyungwoo Song, Qin Wang, Yuxi Zheng

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We study the regularity of semihyperbolic patches of self-similar solutions near sonic lines to a Riemann problem for the two-dimensional (2-D) Euler system. As a result, it is verified that there exists a global solution in the semihyperbolic patch up to the sonic boundary and that the sonic boundary has C1-regularity. The study of the semihyperbolic patches of solutions for the Euler system was initiated by Li and Zheng [Arch. Rational Mech. Anal., 201 (2011), pp. 1069-1096]. This type of solution appears in the transonic flow over an airfoil and Guderley reflection and is common in the numerical configurations of 2-D Riemann problems.

Original languageEnglish (US)
Pages (from-to)2200-2219
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number3
DOIs
StatePublished - Jan 1 2015

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Euler System
2-D Systems
Gas dynamics
Gas Dynamics
Patch
Regularity
Transonic flow
Line
Cauchy Problem
Arches
Airfoils
Transonic Flow
Self-similar Solutions
Arch
Airfoil
Global Solution
Configuration

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "We study the regularity of semihyperbolic patches of self-similar solutions near sonic lines to a Riemann problem for the two-dimensional (2-D) Euler system. As a result, it is verified that there exists a global solution in the semihyperbolic patch up to the sonic boundary and that the sonic boundary has C1-regularity. The study of the semihyperbolic patches of solutions for the Euler system was initiated by Li and Zheng [Arch. Rational Mech. Anal., 201 (2011), pp. 1069-1096]. This type of solution appears in the transonic flow over an airfoil and Guderley reflection and is common in the numerical configurations of 2-D Riemann problems.",
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The regularity of semihyperbolic patches near sonic lines for the 2-d euler system in gas dynamics. / Song, Kyungwoo; Wang, Qin; Zheng, Yuxi.

In: SIAM Journal on Mathematical Analysis, Vol. 47, No. 3, 01.01.2015, p. 2200-2219.

Research output: Contribution to journalArticle

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