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