Global solutions for the Navier-Stokes equations in the rotational framework

Tsukasa Iwabuchi, Ryo Takada

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The existence of global unique solutions to the Navier-Stokes equations with the Coriolis force is established in the homogeneous Sobolev spaces Hs (ℝ3)3 for 1/2 < s < 3/4 if the speed of rotation is sufficiently large. This phenomenon is so-called the global regularity. The relationship between the size of initial datum and the speed of rotation is also derived. The proof is based on the space time estimates of the Strichartz type for the semigroup associated with the linearized equations. In the scaling critical space H1/2(ℝ3)3, the global regularity is also shown.

Original languageEnglish
Pages (from-to)727-741
Number of pages15
JournalMathematische Annalen
Volume357
Issue number2
DOIs
Publication statusPublished - Oct 1 2013
Externally publishedYes

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Global Regularity
Global Solution
Navier-Stokes Equations
Coriolis Force
Homogeneous Space
Unique Solution
Sobolev Spaces
Semigroup
Scaling
Estimate
Framework
Relationships

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Global solutions for the Navier-Stokes equations in the rotational framework. / Iwabuchi, Tsukasa; Takada, Ryo.

In: Mathematische Annalen, Vol. 357, No. 2, 01.10.2013, p. 727-741.

Research output: Contribution to journalArticle

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