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
N1 - Funding Information:
The authors would like to express their sincere gratitude to Professor Hideo Kozono for his valuable suggestions and continuous encouragement. This work was supported by the JSPS Japanese–German Graduate Externship. The second author was supported by Grant-in-Aid for JSPS Fellows 09J01292 .
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.
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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 -