The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas

Qin Wang; Kyungwoo  Song

doi:10.3934/dcds.2016.36.1661

Article Contents

2016, Volume 36, Issue 3: 1661-1675. Doi: 10.3934/dcds.2016.36.1661

This issue Previous Article Lipschitz dependence of viscosity solutions of Hamilton-Jacobi equations with respect to the parameter Next Article On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems

The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas

Qin Wang^1, and
Kyungwoo Song^2,

1.
Department of Mathematics, Yunnan University, Kunming 650091
2.
Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701

Received: October 31, 2014

Revised: February 28, 2015

Published: May 2017

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Abstract

We study the regularity of sonic curves from a two-dimensional Riemann problem for the nonlinear wave system of Chaplygin gas, which is an essential step for the global existence of solutions to the two-dimensional Riemann problems. As a result, we establish the global existence of uniformly smooth solutions in the semi-hyperbolic patches up to the sonic boundary, where the degeneracy of hyperbolicity occurs. Furthermore, we show the $C^1$-regularity of sonic curves.

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Mathematics Subject Classification: 35L65, 35J70, 35R35.

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