Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄ^s_{p, λ,q}(ℝ³) with . By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to . The space FṄ^s_p,λ,q(ℝ³) covers the classical spaces Ḃ^s_q and FḂ^s_p,q(ℝ³) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].