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

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


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