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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics


Author: Raphaël Danchin
Journal: Proc. Amer. Math. Soc. 141 (2013), 1979-1993
MSC (2010): Primary 35Q35, 76B03, 76B70, 35A01
Published electronically: December 11, 2012
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Abstract: We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result of this kind for the inviscid Boussinesq system. In passing, we provide continuation criteria (of independent interest) in the $ N$-dimensional case. In the second part of the paper, our method is adapted to handle the axisymmetric incompressible Euler equations with swirl.


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Raphaël Danchin
Affiliation: Université Paris-Est, LAMA, UMR 8050, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
Email: danchin@univ-paris12.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11591-6
PII: S 0002-9939(2012)11591-6
Received by editor(s): September 15, 2011
Published electronically: December 11, 2012
Communicated by: Walter Craig
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.