Two-Dimensional Riemann Problems for Chaplygin Gas

In this paper we study two-dimensional Riemann problems of the Euler system for Chaplygin gas with initial data being three constant states separated by a Y-type curve. We prove that the general two-dimensional Y-type Riemann problem for the isentropic and irrotational Chaplygin gas admits a global self-similar solution, provided that the three initial states are close enough. Meanwhile, we describe the global wave structure in general cases. Our conclusion extends Lax's result for the one-dimensional Riemann problem of compressible flow to the two-dimensional case for Chaplygin gas.