Global solvability of the navier-stokes equations in spaces based on sum-closed frequency sets

Yoshikazu Giga, Katsuya Inui, Alex Mahalov, Jürgen Saal

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We prove existence of global regular solutions for the 3D Navier-Stokes equations with (or without) Coriolis force for a class of initial data u0 in the space FMσ,δ, i.e., for functions whose Fourier image û0 is a vector-valued Radon measure and that are supported in sumclosed frequency sets with distance δ from the origin. In our main result we establish an upper bound for admissible initial data in terms of the Reynolds number, uniform on the Coriolis parameter ω. In particular this means that this upper bound is linearly growing in δ. This implies that we obtain global-in-time regular solutions for large (in norm) initial data u0 which may not decay at space infinity, provided that the distance δ of the sum-closed frequency set from the origin is sufficiently large.

Original languageEnglish (US)
Pages (from-to)721-736
Number of pages16
JournalAdvances in Differential Equations
Volume12
Issue number7
StatePublished - Dec 1 2007

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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