We study the Cauchy problem of the fractional Navier-Stokes equations in critical Fourier-Besov spaces . 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 case . Moreover, we prove the long time decay of the global solutions in Fourier-Besov spaces.
"Global Well-Posedness and Long Time Decay of Fractional Navier-Stokes Equations in Fourier-Besov Spaces." Abstr. Appl. Anal. 2014 (SI40) 1 - 11, 2014. https://doi.org/10.1155/2014/463639