On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity

Okihiro Sawada, Ryo Takada

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The Cauchy problem of the Euler equations in the whole space is considered with non-decaying initial velocity in the frame work of B∞,11. It is proved that if the initial velocity is real analytic then the solution is also real analytic in spatial variables. Furthermore, a new estimate for the size of the radius of convergence of Taylor's expansion is established. The key of the proof is to derive the suitable estimates for the higher order derivatives of the bilinear terms. It is also shown the propagation of the almost periodicity in spatial variables.

Original languageEnglish
Pages (from-to)2148-2162
Number of pages15
JournalJournal of Functional Analysis
Volume260
Issue number7
DOIs
Publication statusPublished - 2011 Apr 1

Keywords

  • Almost periodicity
  • Analyticity
  • Non-decaying initial velocity
  • The Euler equations

ASJC Scopus subject areas

  • Analysis

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