Global Solvability of the Generalized Boussinesq System with Linear or Nonlinear Buoyancy Force

This paper is devoted to the global solvability of the Boussinesq system with fractional Laplacian (−∆)α in for n ≥ 3, where the buoyancy force has the form |θ|m−1θen with m ≥ 1. By establishing estimates for the difference |θ1|m−1θ1 − |θ2|m−1θ2 in Besov spaces and employing the maximal regularity property of (−∆)α in Lorentz spaces, we prove the following results: under some reasonable assumptions on the exponents α, m, p, r and ρ, if the small initial data of velocity and temperature (or salinity) fall in (where p1 = p for 1 1, then the generalized Boussinesq system admits a unique global strong solution (u, θ) in × (with i = 1, 2 cor-responding to the definition of p1, p2) for m = 1 and in × for m > 1, respectively.