99-20
On the two-dimensional gas expansion for compressible Euler equation II. The case 1 < $\gamma$ < 3
by Jiequan Li
Preprint series: 99-20, 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 the continuation of Preprint 99-19. We take into account the existence of global continuous solutions of two-dimensional gas expansion for compressible Euler equations for the case 1 < $\gamma$ < 3. The flow is governed by a partial differential of second order in the phase space under irrotationality condition, which can be further reduced to three inhomogenous linearly degenerate equations. Then this conclusion is applied to solve the problem that a wedge of gas expands into a vacuum and analyze the occurence of shocks in the interaction of four planar rarefaction waves.
Keywords: two-dimensional gas expansion, global continuous solutions, linearlydegenerate equations, irrotationality condition, the interface of gas and vacuum, planar rarefaction waves
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