Some special solutions of the multidimensional Euler equations in $R^N$

Tianhong Li

doi:10.3934/cpaa.2005.4.757

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2005, Volume 4, Issue 4: 757-762. Doi: 10.3934/cpaa.2005.4.757

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Some special solutions of the multidimensional Euler equations in $R^N$

Tianhong Li^1,

1.
Department of Mathematics, Stanford University, Stanford, CA 94305

Received: January 2005

Revised: May 2005

Published: December 2005

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Abstract

In this paper we give some special solutions, including some blow-up solutions, to the multi-dimensional Euler equations for compressible gas dynamics. We also show that finite energy implies nonexistence of $\delta$-function blow-up for $\gamma>1$.

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Mathematics Subject Classification: 35L60, 35L65.

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