On the global well-posedness for the incompressible four-component chemotaxis-Navier–Stokes equations with gradient-dependent flux limitation in [formula omitted]

Abstract

We consider the four-component chemotaxis-Navier–Stokes system in R2: nt+u⋅∇n=Δn−∇⋅(nf(|∇c|2)∇c)−nm,ct+u⋅∇c=Δc−c+m,mt+u⋅∇m=Δm−nm,ut+(u⋅∇)u+∇P=Δu+(n+m)∇ϕ,∇⋅u=0.Utilizing the Fourier localization technique alongside the inherent structure of the equations, we achieve global well-posedness for a class of rough initial data in the context of the 2D incompressible four-component chemotaxis-Navier–Stokes equations with gradient-dependent flux limitation f(ζ)=Kf⋅(1+ζ)−α2 for α>0.