Elementary Wave Interactions to the Compressible Euler Equations for Chaplygin Gas in Two Dimensions

Abstract

In order to construct global piecewise smooth solutions to two-dimensional (2D) Riemann problems for the compressible Euler equations, it is important to investigate 2D elementary wave interactions. Recently, 2D shock interactions and 2D Riemann problems for the compressible Euler equations for Chaplygin gas have been investigated. In this paper, we study several types of 2D elementary wave interactions of the Chaplygin gas Euler equations. These elementary waves include shock waves, simple waves, and delta waves. Using these elementary wave interactions, global piecewise smooth solutions to several 2D Riemann problems are constructed.