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

Qin Wang; Kyungwoo Songy

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

Qin Wang
, Kyungwoo Songy

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 C¹-regularity of sonic curves.

Original language	English
Pages (from-to)	1661-1675
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems
Volume	36
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2016.36.1661
Publication status	Published - 1 Mar 2016

Keywords

2-D Riemann problem
Bootstrap method
Chaplygin gas
Nonlinear wave system
Regularity

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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 C1-regularity of sonic curves.",

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N2 - 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 C1-regularity of sonic curves.

AB - 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 C1-regularity of sonic curves.

KW - 2-D Riemann problem

KW - Bootstrap method

KW - Chaplygin gas

KW - Nonlinear wave system

KW - Regularity

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ER -

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

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Keywords

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