Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type

Tsukasa Iwabuchi, Ryo Takada

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We consider the initial value problems for the Navier-Stokes equations in the rotational framework. We introduce function spaces Ḃp,qs(R3) of Besov type, and prove the global in time existence and the uniqueness of the mild solution for small initial data in our space Ḃ1,2-1(R3) near BMO-1(R3). Furthermore, we also discuss the ill-posedness for the Navier-Stokes equations with the Coriolis force, which implies the optimality of our function space Ḃ1,2-1(R3) for the global well-posedness.

Original languageEnglish
Pages (from-to)1321-1337
Number of pages17
JournalJournal of Functional Analysis
Volume267
Issue number5
DOIs
Publication statusPublished - Sep 1 2014
Externally publishedYes

Fingerprint

Coriolis Force
Ill-posedness
Global Well-posedness
Function Space
Navier-Stokes Equations
Mild Solution
Initial Value Problem
Optimality
Uniqueness
Imply
Framework

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type. / Iwabuchi, Tsukasa; Takada, Ryo.

In: Journal of Functional Analysis, Vol. 267, No. 5, 01.09.2014, p. 1321-1337.

Research output: Contribution to journalArticle

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