Long-term behaviour in a chemotaxis-fluid system with logistic source

2016/02/01 by Johannes Lankeit, Lankeit, Johannes
Computer Science · Mathematics · Physics and Astronomy · #35B40 #35B65 #35K55 #35Q30 #92C17 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Micro and Nano Robotics

paper · pdf · doi:10.48550/arxiv.1602.00665

openalex publication_date 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the coupled chemotaxis Navier-Stokes model with logistic source terms n_t + u⋅ ∇ n = Δn - χ∇ ⋅ (n ∇ c) + κn - μn² c_t + u⋅ ∇ c = Δc - nc u_t + (u⋅ ∇)u = Δu +∇ P + n∇ Φ+ f, ∇ ⋅ u=0 in a bounded, smooth domain Ω⊂ ℝ³ under homogeneous Neumann boundary conditions for n and c and homogeneous Dirichlet boundary conditions for u and with given functions f∈ L^∞(Ω×(0,∞)) satisfying certain decay conditions and Φ∈ C^1+β(Ω) for some β∈(0,1). We construct weak solutions and prove that after some waiting time they become smooth and finally converge to the semi-trivial steady state (\fracκμ,0,0). Keywords: chemotaxis, Navier-Stokes, logistic source, boundedness, large-time behaviour

Citations

• How far do chemotaxis-driven forces influence regularity in the\n Navier-Stokes system?
• Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities

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