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arXiv · 1412.1212

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

Qin Wang·Kyungwoo Song
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Abstract

We study the regularity of sonic curves to 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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Qin Wang, Kyungwoo Song. 2014-12-03. The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas. https://arxiv.org/abs/1412.1212

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