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Simple waves and a characteristic decomposition of the two-dimensional compressible Euler equations. (English) Zbl 1113.76080

Summary: We present a characteristic decomposition of the potential flow equation in the self-similar plane. The decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for adiabatic Euler system. This result is a generalization of well-known result on two-dimensional steady potential flow and of a recent similar result on the pressure gradient system.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
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