Global existence and boundedness in a chemotaxis-Stokes system with slow p-Laplacian diffusion

2018/09/10 by Weirun Tao, Yuxiang Li, Tao, Weirun +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #35K55 #35Q35 #35Q92 #92C17 #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1809.03310

openalex publication_date 2018/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with a boundary-value problem in three-dimensional smooth bounded convex domains for the coupled chemotaxis-Stokes system with slow p-Laplacian diffusion \ \beginaligned amp;n_t+u⋅∇ n=∇⋅(|∇ n|^p-2∇ n)-∇⋅(n∇ c), amp;x∈Ω, tgt;0, amp;c_t+u⋅∇ c=Δc-nc,amp;x∈Ω, tgt;0, amp;u_t=Δu+∇ P+n∇ϕ,amp;x∈Ω, tgt;0, amp;∇⋅ u=0, amp;x∈Ω, tgt;0, \endaligned . where ϕ∈ W^2,∞(Ω) is the gravitational potential. It is proved that global bounded weak solutions exist whenever p>(23)/(11) and the initial data (n₀,c₀,u₀) are sufficiently regular satisfying n₀≥ 0 and c₀≥ 0.

Citations

• A user’s guide to PDE models for chemotaxis

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