LAUSR

Abstract In this paper, we consider the following chemotaxis-fluid model with singular sensitivity and logistic source { n t + u ⋅ ∇ n = Δ n − χ ∇ ⋅ ( n c ∇ c ) + r n − μ n k , x ∈ Ω , t > 0 , c t + u ⋅ ∇ c = Δ c − c + n , x ∈ Ω , t > 0 , u t + λ ( u ⋅ ∇ ) u = Δ u + ∇ P + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 in a bounded domain Ω ⊂ R N ( N = 2 , 3 ) with smooth boundary ∂Ω. Under the non-flux boundary conditions for n and c, and the non-slip boundary condition for u, we establish the global boundedness and the time-decay rates of the classical solutions for any k > 1 provided that χ satisfies suitable restrictions.