### 1999-19

#### On the two-dimensional gas expansion for compressible Euler equation I. The case $\gamma$ = 1

by Jiequan Li.

Series: 1999-19, Preprints

MSC:
35L65 Conservation laws
35L67 Shocks and singularities
65M99 None of the above, but in this section
76N15 Gas dynamics, general

Abstract:
This paper is concerned with the existence of global
continuous solutions of gas expansion into a vacuum for
compressible Euler equations with $\gamma$ = 1. We prove
that the flow is governed by two inhomogeneous linearly
degenerate equations in the phase space under irrotationality
condition. Then this conclusion is applied to solve the
problem that a wedge of gas expands into a vacuum, which is
actually a Goursat problem for these two equations in the
supersonic domain.

Keywords:
two-dimensional gas expansion, compressible Euler equation, global continuous solutions, linearly degenerate equations, irrotationality condition