Global well-posedness for the two-dimensional coupled chemotaxis-generalized Navier-Stokes system with logistic growth

Abstract

In this paper, we investigate Cauchy problem for the two-dimensional incompressible chemotaxis-Navier-Stokes equations with the lower fractional diffusion{∂tn+u⋅∇n−Δn=−∇⋅(n∇c)+λn−μn2,∂tc+u⋅∇c−Δc=−cn,∂tu+u⋅∇u+Λ2αu+∇P=−n∇ϕ, where Λ:=(−Δ)12 and α∈[12,1]. We obtain the global-in-time existence and uniqueness of weak solution to the equations for a class of large initial data by making use of the coupled structure of system and damping effect of the logistic source, and developing the L43(R2) estimate for vorticity.