Abstract
We study the Cauchy problem of the fractional Navier-Stokes equations in critical Fourier-Besov spacesFB˙p,q1-2β+3/p′. Some properties of Fourier-Besov spaces have been discussed, and we prove a general global well-posedness result which covers some recent works in classical Navier-Stokes equations. Particularly, our result is suitable for the critical caseβ=1/2. Moreover, we prove the long time decay of the global solutions in Fourier-Besov spaces.
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