A new result for global solvability to a two-dimensional attraction-repulsion Navier-Stokes system with consumption of chemoattractant

Abstract

In this paper, we study an attraction-repulsion Navier-Stokes system with consumption of chemoattractant: nt+u⋅∇n=Δn−χ∇⋅(n∇c)+ξ∇⋅(n∇v); ct+u⋅∇c=Δc−nc; τvt+u⋅∇v=Δv−v+n; ut+κ(u⋅∇)u=Δu+∇P+n∇ϕ; ∇⋅u=0, x∈Ω, t>0 in a bounded and smooth domain Ω⊂R2 with no-flux/Dirichlet boundary conditions, where χ,ξ are positive constants, τ∈{0,1}. We present the global existence of attraction-repulsion Navier-Stokes system with τ=1 and global boundedness of attraction-repulsion Navier-Stokes system with τ=0, and our result generalize the result obtained in previously known ones and partly result is new.