Global existence in a three-dimensional chemotaxis-Stokes system with p-Laplacian diffusion and singular sensitivity

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Nonlinear Analysis-Real World Applications Pub Date : 2025-02-24 DOI:10.1016/j.nonrwa.2025.104339

Ruina He, Zhongping Li

引用次数: 0

Abstract

This paper considers the following chemotaxis-Stokes system

(\begin{matrix} n_{t} + u \cdot \nabla n = \nabla \cdot ({(\nabla n)}^{p - 2} \nabla n) - χ \nabla \cdot (\frac{n}{c} \nabla c) + n (r - μ n^{δ}), \\ c_{t} + u \cdot \nabla c = Δ c - n c, \\ u_{t} = Δ u + \nabla P + n \nabla Φ \end{matrix})

in a smooth bounded domain

Ω \subset R^{3}

with no-flux/no-flux/Dirichlet boundary conditions. It is shown that there exists a global weak solution when

p \geq 2

and

δ > \frac{3}{2}

, which removes the restriction

p > min (\frac{6 δ + 1}{2 (2 δ - 1)}, \frac{2 δ (δ + 2)}{(2 δ + 3) (δ - 1)})

and improves the result of the paper (Han and Liu, 2023).

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本文考虑以下趋化-斯托克斯系统 nt+u⋅∇n=∇⋅∇np-2∇n-χ∇⋅(nc∇c)+nr-μnδ、ct+u⋅∇c=Δc-nc,ut=Δu+∇P+n∇Φ，在光滑有界域Ω⊂R3 中，无流/无流/德里克特边界条件。结果表明，当 p≥2 和 δ>32 时，存在全局弱解，从而消除了 p>min6δ+122δ-1,2δδ+22δ+3δ-1 的限制，改进了论文的结果 (Han and Liu, 2023)。

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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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.