Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational flux term

2016/04/01 by Xinru Cao, Cao, Xinru
Biochemistry, Genetics and Molecular Biology · Mathematics · #35D05 #35K45 #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1604.00211

openalex publication_date 2016/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The coupled chemotaxis fluid system \ n_t=Δn-∇⋅(nS(x,n,c)⋅∇ c)-u⋅∇ n, · amp;(x,t)∈ Ω× (0,T),
c_t=Δc-nc-u⋅∇ c , · amp;(x,t)∈Ω× (0,T),
u_t=Δu-κ(u⋅∇)u+∇ P+n∇ϕ, · amp;(x,t)∈Ω× (0,T),
∇⋅ u=0, · amp;(x,t)∈Ω× (0,T), .(⋆) is considered under the no-flux boundary conditions for n,c and the Dirichlet boundary condition for u on a bounded smooth domain Ω⊂ℝ^N (N=2,3), κ=0,1. We assume that S(x,n,c) is a matrix-valued sensitivity under a mild assumption such that |S(x,n,c)|

Citations

• Large-data global generalized solutions in a chemotaxis system with\n tensor-valued sensitivities

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