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

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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 ℝn , n ≥ 3 . For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator type estimates in our weak spaces.

Original languageEnglish
Pages (from-to)693-725
Number of pages33
JournalJournal of Evolution Equations
Volume8
Issue number4
DOIs
Publication statusPublished - Nov 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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