The regularity of semi-hyperbolic patches at sonic lines for the pressure gradient equation in gas dynamics

Qin Wang, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We study the uniformregularity of semi-hyperbolic patches of self-similar solutions near sonic lines to a general Riemann problem for the pressure gradient equation. This type of solution, in which one family of characteristics starts on a sonic line and ends on a transonic shock wave, is common for the Riemann problems for the Euler system in two space dimensions. The global existence of smooth solutions was established in Song and Zheng [Disc. Cont. Dyna. Syst., 24 (2009),1365-1380], but the smoothness near the sonic lines is not clear. We establish that the smooth solutions are uniformly smooth up to their sonic boundaries, and that the sonic lines are C1 continuous.

Original languageEnglish (US)
Pages (from-to)385-402
Number of pages18
JournalIndiana University Mathematics Journal
Volume63
Issue number2
DOIs
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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