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

Abstract

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.

Semi-hyperbolic patches of solutions to the two-dimensional compressible magnetohydrodynamic equations

“…For semi-hyperbolic patches of solutions to some other type of hyperbolic conservation laws, the readers can see [9,10,11]. Song et al [24,28] also studied the regularity of semi-hyperbolic patches near sonic lines. There are also some other ways to construct such a flow patch.…”