Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data

Yoshikazu Giga, Katsuya Inui, Alex Mahalov, Jürgen Saal

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

We establish a global existence result for the rotating Navier-Stokes equations with nondecaying initial data in a critical space which includes a large class of almost periodic functions. We introduce the scaling invariant function space which is defined as the divergence of the space of 3 × 3 fields of Fourier transformed finite Radon measures. The smallness condition on initial data for global existence is explicitly given in terms of the Reynolds number. The condition is independent of the size of the angular velocity of rotation.

Original languageEnglish (US)
Pages (from-to)2775-2791
Number of pages17
JournalIndiana University Mathematics Journal
Volume57
Issue number6
DOIs
StatePublished - Dec 1 2008

Keywords

  • Almost periodic initial data
  • Coriolis force
  • Global solutions
  • Navier-Stokes equations
  • Radon measures

ASJC Scopus subject areas

  • Mathematics(all)

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