99-19
On the two-dimensional gas expansion for compressible Euler equation I. The case $\gamma$ = 1
by Jiequan Li
Preprint series: 99-19, Preprints
- MSC:
- 35L65 Conservation laws
- 35L67 Shocks and singularities, See also {58C27, 76L05}
- 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
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