# American Institute of Mathematical Sciences

March  2015, 14(2): 609-622. doi: 10.3934/cpaa.2015.14.609

## Local and global existence results for the Navier-Stokes equations in the rotational framework

 1 Department of Mathematics, Zhejiang University, Hangzhou 310027 2 Department of Mathematics, Fudan University, Shanghai, 200433, China 3 Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt

Received  June 2014 Revised  October 2014 Published  December 2014

Consider the equations of Navier-Stokes in $R^3$ in the rotational setting, i.e. with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided only the horizontal components of the initial data are small with respect to the norm the Fourier-Besov space $\dot{FB}_{p,r}^{2-3/p}(R^3)$, where $p \in [2,\infty]$ and $r \in [1,\infty)$.
Citation: Daoyuan Fang, Bin Han, Matthias Hieber. Local and global existence results for the Navier-Stokes equations in the rotational framework. Communications on Pure & Applied Analysis, 2015, 14 (2) : 609-622. doi: 10.3934/cpaa.2015.14.609
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