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

Research output: Contribution to journalArticle

10 Citations (Scopus)

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

Fingerprint

Blow-up Criterion
L-p space
Local Existence
Besov Spaces
Euler Equations
Perfect Fluid
Commutator
Incompressible Fluid
Function Space
Logarithmic
Estimate
Standards

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type. / Takada, Ryo.

In: Journal of Evolution Equations, Vol. 8, No. 4, 01.11.2008, p. 693-725.

Research output: Contribution to journalArticle

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