2018/05/14 by Yulan Wang, Michael Winkler, Wang, Yulan +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #(2010): 92C17 (primary) #35B65 #35K55 #35Q30 #35Q92 (secondary) #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.1805.05263
openalex publication_date 2018/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with convergence of solutions to a class of parabolic Keller-Segel systems, possibly coupled to the (Navier-)Stokes equations in the framework of the full model \ ∂t nε + uε ⋅ ∇ nε · amp;= · amp; Δnε - ∇ ⋅ ( nε S(x, nε, cε)⋅∇ cε) + f(x, nε, cε),
ε∂t cε + uε⋅∇ cε · amp;= · amp; Δcε - cε + nε ,
∂t uε + κ(uε⋅∇) uε · amp;= · amp; Δuε + ∇ Pε + nε ∇ϕ, ∇⋅ uε=0 . to solutions of the parabolic-elliptic counterpart formally obtained on taking ε\searrow 0. In smoothly bounded physical domains Ω⊂ \mathbb RN with N≥ 1, and under appropriate assumptions on the model ingredients, we shall first derive a general result which asserts certain strong and pointwise convergence properties whenever asserting that supposedly present bounds on ∇ cε and uε are bounded in Lλ((0,T);Lq(Ω)) and in L^∞((0,T);Lr(Ω)), respectively, for some λ∈ (2,∞], q>N and r>max\2,N\ such that \frac1λ+(N)/(2q)