Global solutions to Keller-Segel-Navier-Stokes equations with a class of large initial data in critical Besov spaces.

In this article, we consider the Cauchy problem to Keller-Segel equations coupled to the incompressible Navier-Stokes equations. Using the Fourier frequency localization and the Bony paraproduct decomposition, let u F:= e tΔ u0; we prove that there exist 2 positive constants σ0 and C0 such that if the gravitational potential [ABSTRACT FROM AUTHOR]