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

Daoyuan Fang; Bin Han; Matthias Hieber

doi:10.3934/cpaa.2015.14.609

Article Contents

2015, Volume 14, Issue 2: 609-622. Doi: 10.3934/cpaa.2015.14.609

This issue Previous Article $W$-Sobolev spaces: Higher order and regularity Next Article A note on the unique continuation property for fully nonlinear elliptic equations

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
3.
Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt

Received: June 2014

Revised: October 2014

Published: March 2015

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Abstract

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 $r \in [1,\infty)$.

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Mathematics Subject Classification: 35Q35, 76D03, 76D05.

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