Abstract In this paper, we consider the chemotaxis-consumption system on a bounded smooth domain Ω ⊂ R n, n = 2, 3 R^n, n=2, 3, with fluid coupling ρ t + u ⋅ ∇ ρ − ∇ ⋅ (D (ρ) ∇ ρ) = ∇ ⋅ (ρ S (x, ρ, c) ⋅ ∇ c), u ⋅ ∇ c − Δ c = − ρ c, u t + κ (u ⋅ ∇) u − Δ u + ∇ π = ρ ∇ Φ, ∇ ⋅ u = 0, casesₓ+u - (D () ) = (S (x, , c) c), \\ u c-c=- c, \\ uₓ+ (u) u-u+ =, u=0, cases subject to the boundary conditions ν ⋅ (D (ρ) ∇ ρ + ρS (x, ρ, c) ∇ c) | ∂Ω = 0, (ν ⋅ ∇ c + c) | ∂Ω = γ
Kim et al. (2026) studied this question.