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Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type

Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type We introduce Besov type function spaces, based on the weak L p -spaces instead of the standard L p -spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations of perfect incompressible fluid in $${\mathbb{R}}^n , n \geq 3$$ . For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator type estimates in our weak spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type

Journal of Evolution Equations , Volume 8 (4) – Nov 1, 2008

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Birkhaueser
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-008-0403-6
Publisher site
See Article on Publisher Site

Abstract

We introduce Besov type function spaces, based on the weak L p -spaces instead of the standard L p -spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations of perfect incompressible fluid in $${\mathbb{R}}^n , n \geq 3$$ . For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator type estimates in our weak spaces.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Nov 1, 2008

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