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

Ryo Takada

Research output: Contribution to journalArticlepeer-review

14 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 - 2008 Nov 1

Keywords

  • Besov spaces of weak type
  • Blow-up criterion
  • Commutator estimates
  • Euler equations
  • Littlewood-Paley decomposition
  • Local existence

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Fingerprint Dive into the research topics of 'Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type'. Together they form a unique fingerprint.

Cite this