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 (−Δ) α in for n ≥ 2, where the convective term has the form (| u | m −1 u )·∇ u for m ≥ 1. By establishing the estimates for the difference in homogeneous Besov spaces and employing the maximal regularity property of (−Δ) α 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.