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

摘要

> 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 t Δ u ₀ ; we prove that there exist 2 positive constants σ ₀ and C ₀ such that if the gravitational potential ? ∈ B ˙ p , 1 3 / p ( R 3 ) and the initial data ( u ₀ , n