Global Well-Posedness for the 2D Keller-Segel-Navier-Stokes System with Fractional Diffusion.

In this paper, we consider Cauchy problem for the 2D incompressible Keller-Segel-Navier-Stokes equations with the fractional diffusion { ∂ t n + u ⋅ ∇ n − Δ n = − ∇ ⋅ (n ∇ c) − n 3 , ∂ t c + u ⋅ ∇ c − Δ c = − c + n , ∂ t u + u ⋅ ∇ u + ∧ 2 α u + ∇ P = − n ∇ ϕ , where ∧ : = (− Δ) 1 2 and α ∈ [ 1 2 , 1 ] . We get the global well-posedness for the above system with the rough initial data by a new priori estimate of the solutions. [ABSTRACT FROM AUTHOR]