# American Institute of Mathematical Sciences

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March  2016, 36(3): 1661-1675. doi: 10.3934/dcds.2016.36.1661

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

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

Received  November 2014 Revised  March 2015 Published  August 2015

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.
Citation: Qin Wang, Kyungwoo Song. The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1661-1675. doi: 10.3934/dcds.2016.36.1661
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