Global well-posedness and ill-posedness for the Navier–Stokes equations with the Coriolis force in function spaces of Besov type
Global well-posedness and ill-posedness for the Navier–Stokes equations with the Coriolis force in function spaces of Besov type
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DOI：
10.1016/j.jfa.2014.05.022
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发表时间：
2014-09
影响因子：
1.7
通讯作者：
T. Iwabuchi;Ryo Takada
中科院分区：
文献类型：
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作者：
T. Iwabuchi;Ryo Takada
本文在转动框架下考虑Navier-Stokes方程的初值问题。引入Besov型函数空间B stecp，qs（R3），证明了在BMO-1（R3）附近，在小初值条件下，该空间B stec 1，2 - 1（R3）中温和解的整体存在性和唯一性.此外，我们还讨论了具有科里奥利力的Navier-Stokes方程的不适定性，这意味着我们的函数空间B stec 1，2− 1（R 3）对于整体适定性是最优的.
We consider the initial value problems for the Navier–Stokes equations in the rotational framework. We introduce function spaces B˙ p, q s (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˙ 1, 2− 1 (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˙ 1, 2− 1 (R 3) for the global well-posedness.