具有慢 p-Laplacian 扩散和旋转的三维趋化-斯托克斯系统弱解的有界性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-19 DOI:10.1016/j.nonrwa.2024.104164

Haolan He, Zhongping Li

引用次数: 0

摘要

本文考虑以下具有一般灵敏度和旋转 nt+u⋅∇n=∇⋅(|∇n|p-2∇n)-∇(nS(x,n,c)∇c),x∈Ω,t> 的趋化-斯托克斯系统；0,ct+u∇c=Δc-nc,x∈Ω,t>0,ut+∇P=Δu+n∇j,x∈Ω,t>0,∇⋅u=0,x∈Ω,t>0在具有零流动边界和无滑动边界条件的光滑有界域Ω∈R3 中。我们证明了在 43p+α>72-63 和 p>2 条件下，具有 p-Laplacian 扩散的三维 chemotaxis-Stokes 系统初始边界值问题弱解的有界性，从而改进了论文 [Chen et al.，76 (2024) 103996；Zhuang 等，Nonlinear Anal.Real World Appl.Equ., 268(11) (2020) 6879-6919]，并将论文[Jin, J. Differ. Equ. 287 (2021) 148-184] 的结果扩展到具有一般敏感性和旋转的趋化系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Boundedness of weak solutions to a 3D chemotaxis-Stokes system with slow p−Laplacian diffusion and rotation

In this paper, we consider the following chemotaxis-Stokes system with general sensitivity and rotation $(\begin{matrix} n_{t} + u \cdot \nabla n = \nabla \cdot ({| \nabla n |}^{p - 2} \nabla n) - \nabla \cdot (n S (x, n, c) \nabla c), & x \in Ω, t > 0, \\ c_{t} + u \cdot \nabla c = Δ c - n c, & x \in Ω, t > 0, \\ u_{t} + \nabla P = Δ u + n \nabla ϕ, & x \in Ω, t > 0, \\ \nabla \cdot u = 0, & x \in Ω, t > 0 \end{matrix})$ in a smooth bounded domain $Ω \in R^{3}$ with zero-flux boundary and no-slip boundary condition. We prove the boundedness of the weak solutions to the initial–boundary value problem of the 3D chemotaxis-Stokes system with $p -$ Laplacian diffusion if $\frac{4}{3} p + α > \frac{7}{2} - \frac{\sqrt{6}}{3}$ and $p > 2$ , which improves the results of papers [Chen et al., Nonlinear Anal. Real World Appl., 76 (2024) 103996; Zhuang et al., Nonlinear Anal. Real World Appl., 56 (2020) 103163 and Tao et al., J. Differ. Equ., 268(11) (2020) 6879–6919] and extends the result of the paper [Jin, J. Differ. Equ. 287 (2021) 148–184] to the chemotaxis system with general sensitivity and rotation.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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