2017/06/07 by Zheng, Jiashan, Li, Yanyan, Zou, Xinhua +2
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.02022
This paper is concerned with the following quasilinear chemotaxis--Navier--Stokes system with nonlinear diffusion and rotation \ nt+u⋅∇ n=Δnm-∇⋅(nS(x,n,c)⋅∇ c), x∈ Ω, t · gt;0, ct+u⋅∇ c=Δc-nc, x∈ Ω, t · gt;0,
ut+κ(u ⋅ ∇)u+∇ P=Δu+n∇ ϕ, x∈ Ω, t · gt;0,
∇⋅ u=0, x∈ Ω, t · gt;0.\eqno(CNF) is considered under the no-flux boundary conditions for n, c and the Dirichlet boundary condition for u in a three-dimensional convex domain Ω⊆ ℝ3 with smooth boundary, which describes the motion of oxygen-driven bacteria in a fluid. Here % Ω⊆ ℝ3 is a , κ∈ ℝ and S denotes the strength of nonlinear fluid convection and a given tensor-valued function, respectively. Assume m>(10)/(9) and S fulfills |S(x,n,c)| ≤ S0(c) for all (x,n,c)∈ Ω × [0, ∞)×[0, ∞) with S0(c) nondecreasing on [0,∞), then for any reasonably regular initial data, the corresponding initial-boundary problem (CNF) admits at least one global weak solution.