Two-dimensional pseudo-steady supersonic flow around a sharp corner for the generalized Chaplygin gas

Abstract

In this paper, the expansion problem which arises in a two-dimensional (2D) isentropic pseudo-steady supersonic flow expanding into vacuum around a sharp corner for the generalized Chaplygin gas is studied. This expanding problem catches the interaction of an incomplete centered simple wave with a backward planar rarefaction wave and the interaction of a non-planar simple wave with a rigid wall boundary of the 2D self-similar Euler equations. Using the methods of characteristic decompositions and invariant regions, we get the hyperbolicity in the wave interaction domains and prior $ C^{1} $ estimates of solutions to the two interaction problems. It follows the global existence of the solution up to infinity of the gas expansion problem.

Keywords

• two-dimensional euler equations
• generalized chaplygin gas
• pseudo-steady supersonic flow
• incomplete centered simple wave
• interaction of simple wave with rigid wall boundary