, Volume 267, Issue 1, pp 1-12
Date: 05 May 2006

Simple Waves and a Characteristic Decomposition of the Two Dimensional Compressible Euler Equations

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Abstract

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 the adiabatic Euler system. This result is a generalization of the well-known result on 2-d steady potential flow and a recent similar result on the pressure gradient system.

Research partially supported by NSF of China with No. 10301022, NSF from Beijing Municipality, Fok Ying Tong Educational Foundation, and the Key Program from Beijing Educational Commission with no. KZ200510028018.
Research partially supported by NSF-DMS-0305497, 0305114.
Communicated by P. Constantin