Global Solvability of the Generalized Navier−Stokes System in Critical Besov Spaces

This paper is devoted to the global solvability of the Navier−Stokes system with a fractional Laplacian −Δα in Rn for n≥2, where the convective term has the form um−1u·∇u for m≥1. By establishing the estimates for the difference u1m−1u1−u2m−1u2 in homogeneous Besov spaces and employing the maximal regularity property of −Δα in Lorentz−Besov spaces, we prove global existence and uniqueness of the strong solution of the Navier−Stokes system in critical Besov spaces for both m=1 and m>1.