Counterexamples of commutator estimates in the besov and the triebel - Lizorkin spaces related to the euler equations

Ryo Takada

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

This paper deals with the Kato.Ponce - type commutator estimates in the Besov space Bs p, q(ℝn) and the Triebel - Lizorkin space Fs p, q(ℝn) related to the Euler equations describing the motion of perfect incompressible fluids. We investigate the relation between the optimal bound of the commutator estimates and the solvability of the Euler equations. In particular, we show that these commutator estimates fail in Bs p, q(ℝn) and F s p, q(ℝn) with the critical differential order s = n/p + 1 and various exponents p and q.

Original languageEnglish
Pages (from-to)2473-2483
Number of pages11
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number6
DOIs
Publication statusPublished - 2010 Dec 1

Keywords

  • Commutator estimates
  • Incompressible Euler equations
  • The Besov spaces
  • The Triebel - Lizorkin spaces

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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