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Existence of a weak solution for the semigeostrophic equation with integrable initial data

Published online by Cambridge University Press:  12 July 2007

M. C. Lopes Filho  and
H. J. Nussenzveig Lopes
M. C. Lopes Filho
Affiliation:
Departamento de Matematica, IMECC-UNICAMP, Caixa Postal 6065, Campinas, SP 13083-970, Brasil ([email protected])
H. J. Nussenzveig Lopes
Affiliation:
Departamento de Matematica, IMECC-UNICAMP, Caixa Postal 6065, Campinas, SP 13083-970, Brasil ([email protected])
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Abstract

In this article we present a proof of existence of a weak solution for the semigeostrophic system of equations, formulated as an active scalar transport equation with Monge-Ampère coupling, with initial data in . This is an extension of a 1998 result due to Benamou and Brenier, who proved existence with initial data in .

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 2 , April 2002 , pp. 329 - 339
Copyright
Copyright © Royal Society of Edinburgh 2002

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