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

被引:59
作者
Iwabuchi, Tsukasa [2 ]
Takada, Ryo [1 ]
机构
[1] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan
[2] Chao Univ, Fac Sci & Engn, Dept Math, Bunkyo Ku, Kasuga, Tokyo 1128551, Japan
关键词
The Navier Stokes equations; The Coriolis force; Global well-posedness; Ill-posedness; SOLVABILITY; DISPERSION; REGULARITY; EULER;
D O I
10.1016/j.jfa.2014.05.022
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the initial value problems for the Navier Stokes equations in the rotational framework. We introduce function spaces <(B)over dot>(s)(p,q)(R-3) ) of Besov type, and prove the global in time existence and the uniqueness of the mild solution for small initial data in our space <(B)over dot>(-1)(1.2)(R-3) near BMO-1(R-3). Furthermore, we also discuss the ill-posedness for the Navier Stokes equations with the Coriolis force, which implies the optimality of our function space <(B)over dot>(-1)(1.2)(R-3) for the global well-posedness. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:1321 / 1337
页数:17
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