Abstract:

We consider the Cauchy problem of fractional Navier-Stokes equations with the Coriolis force. Combining the $L^p-L^q$ and $\dot{H}^{\frac{5}{2}-2\alpha}-L^q$ smooth estimates of semiggroup $S$, it is proved that the well-posedness of the fractional Navier-Stokes equations with the Coriolis force and these equations possess a unique global mild solution for arbitrary speed of rotation provided the initial data $u_0$ is small enough in $\dot{H}_{\sigma}^{\frac{5}{2}-2\alpha}(\mathbb{R}^3)$.

Key words: Global well-posedness, Fractional Navier-Stokes equation, Homogeneous Sobolev spaces, Coriolis force