MR3468733
Tsukasa IWABUCHI and Ryo TAKADA
Tsukasa IWABUCHI and Ryo TAKADA
Dispersive Effect of the Coriolis Force and the Local Well-Posedness for the Navier-Stokes Equations in the Rotational Framework
Funkcialaj Ekvacioj. Serio Internacia
58
2015
365--385
http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-3/58_365.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3468733
We consider the initial value problems for the Navier-Stokes equations with the Coriolis force. We prove the local in time existence and uniqueness of the mild solution for every $\Omega\in\mathbb{R}\setminus\{0\}$ and $u_0\in\dot{H}^s(\mathbb{R}^3)^3$ with $s>1/2$. Furthermore, we give a lower bound of the existence time in terms of $|\Omega|$ and $\|u_0\|_{\dot{H}^s}$. It follows from our lower bound that the existence time $T$ of the solution can be taken arbitrarily large provided the speed of rotation $|\Omega|$ is sufficiently fast.
Navier-Stokes equations, Coriolis force, Local well-posedness.
76U05, 76D03.
58-365
2015
Dispersive Effect of the Coriolis Force and the Local Well-Posedness for the Navier-Stokes Equations in the Rotational Framework
Tsukasa IWABUCHI and Ryo TAKADA
Tsukasa IWABUCHI and Ryo TAKADA
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