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

by Jiequan Li.

Series: 1999-19, Preprints

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

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.

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