The expansion of gas from a wedge with small angleinto a vacuum

Weixia Zhao

doi:10.3934/cpaa.2013.12.2319

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2013, Volume 12, Issue 5: 2319-2330. Doi: 10.3934/cpaa.2013.12.2319

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The expansion of gas from a wedge with small angle into a vacuum

Weixia Zhao^1,

1.
School of Mathematical Sciences, Fudan University, Shanghai 200433

Received: May 31, 2012

Revised: September 30, 2012

Published: August 2013

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Abstract

In this paper, the problem of the expansion of a wedge of gas into vacuum is investigated. Let $\theta$ be the half angle of the wedge. For a given $\bar{\theta}$ determined by the adiabatic exponent $\gamma$, we prove the global existence of the solution through the direct approach in the case $\theta\leq\bar{\theta}$, extending the previous result obtained by Li, Yang and Zheng. Our analysis relies on the special symmetric structure of the characteristic form as well as characteristic decompositions.

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Mathematics Subject Classification: Primary: 35L65; Secondary: 35J70, 35R35.

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