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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: [email protected]
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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.

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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