Global boundedness in a two-dimensional chemotaxis-Navier–Stokes system with double chemical signals and nonlinear diffusion
Year: 2025
Type: article
Abstract: This paper investigates the following chemotaxis-Navier–Stokes system with double chemical signals and nonlinear diffusion n t + u ⋅ ∇ n = ∇ ⋅ ( D ( n ) ∇ n ) − χ ∇ ⋅ ( n ∇ c ) + ξ ∇ ⋅ ( n ∇ v ) , x ∈ Ω , t > 0 , c t + u ⋅ ∇ c = Δ c − n c , x ∈ Ω , t > 0 , v t + u ⋅ ∇ v = Δ v − v + n , x ∈ Ω , t > 0 , u t + κ ( u ⋅ ∇ ) u = Δ u + ∇ P + n ∇ Φ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 in a smooth bounded domain Ω ⊂ R 2 with no-flux/no-flux/no-flux/no-slip boundary conditions, where χ > 0 , ξ < 0 and κ ∈ R are given constants. D is a given function satisfying D ( s ) ≥ ( s + 1 ) m − 1 for all s ≥ 0 . We obtain the boundedness of the classical solution to the initial–boundary value problem of the 2D chemotaxis-Navier–Stokes system if m > 1 , which implies that saturation effect can prevent blow-up arising from the chemotaxis-Navier–Stokes system without any smallness condition on the initial mass.
Authors: Wang Luo, Zhongping Li
Institution: China West Normal University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,780
Funder: China West Normal University
Award: G8386071428
OpenAlex ID: W4410911842