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 | |
| Publication status | Published - Sep 1 2014 |
| Externally published | Yes |
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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 journal › Article
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TY - JOUR
T1 - Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type
AU - Iwabuchi, Tsukasa
AU - Takada, Ryo
PY - 2014/9/1
Y1 - 2014/9/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84904113162&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84904113162&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2014.05.022
DO - 10.1016/j.jfa.2014.05.022
M3 - Article
AN - SCOPUS:84904113162
VL - 267
SP - 1321
EP - 1337
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 5
ER -