2016/01/15 by Xinru Cao, Cao, Xinru, Johannes Lankeit +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #35B35 #35B40 35Q35 #35K55 #92C17 #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.1601.03897
openalex publication_date 2016/01/15 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
The coupled chemotaxis fluid system \ nt=Δn-∇⋅(n S(x,n,c)⋅∇ c)-u⋅∇ n, · amp;(x,t)∈ Ω× (0,T), ct=Δc-nc-u⋅∇ c, · amp;(x,t)∈Ω× (0,T), ut=Δu-(u⋅∇ )u+∇ P+n∇Φ, ∇⋅ u=0, · amp;(x,t)∈Ω× (0,T), ∇ c⋅ν=(∇ n-nS(x,n,c)⋅∇ c)⋅ν=0, u=0, · amp;(x,t)∈ ∂Ω× (0,T), n(x,0)=n0(x), c(x,0)=c0(x), u(x,0)=u0(x) · amp; x∈Ω, . where S∈ (C2(Ω× [0,∞)2))N× N, is considered in a bounded domain Ω⊂ℝN, N∈\2,3\, with smooth boundary. We show that it has global classical solutions if the initial data satisfy certain smallness conditions and give decay properties of these solutions.