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

doi:10.1016/j.jfa.2014.05.022

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

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

30 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 language	English
Pages (from-to)	1321-1337
Number of pages	17
Journal	Journal of Functional Analysis
Volume	267
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2014.05.022
Publication status	Published - Sep 1 2014

All Science Journal Classification (ASJC) codes

Analysis

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

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.",

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AB - 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.

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