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Remarks on spherically symmetric solutions of the compressible Euler equations

Published online by Cambridge University Press:  14 November 2011

Gui-Qiang Chen
Gui-Qiang Chen
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208, U.S.A. e-mail: gqchen@math.nwu.edu
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Abstract

Some evidence indicates that spherically symmetric solutions of the compressible Euler equations blow up near the origin at some time under certain circumstances (cf. [4,19]). In this paper, we observe a criterion for L∞ Cauchy data of arbitrarily large amplitude to ensure the existence of L∞ spherically symmetric solutions in the large, which model outgoing blast waves and large-time asymptotic solutions. The equilibrium states of the solutions and their asymptotic decay to such states are analysed. Some remarks on global spherically symmetric solutions are discussed.

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Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 243 - 259
Copyright
Copyright © Royal Society of Edinburgh 1997

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