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

TL;DR

This paper proves the global existence and C^1 regularity of sonic curves in solutions to a 2D Riemann problem for the nonlinear wave system of Chaplygin gas, advancing understanding of solution smoothness near degeneracy points.

Contribution

It establishes the global existence of smooth solutions up to the sonic boundary and proves the C^1 regularity of sonic curves for the first time.

Findings

Global smooth solutions exist up to the sonic boundary.

Sonic curves are proven to be C^1 continuous.

Degeneracy of hyperbolicity is managed in the analysis.

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.