Global well-posedness and long time decay of fractional Navier-Stokes equations in Fourier-Besov spaces (Q1724176)

Summary: We study the Cauchy problem of the fractional Navier-Stokes equations in critical Fourier-Besov spaces \(F \dot{B}_{p, q}^{1 - 2 \beta + 3 / p'}\). 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 case \(\beta = 1 / 2\). Moreover, we prove the long time decay of the global solutions in Fourier-Besov spaces.