带有通量限制机制的三维趋化-Navier-Stokes 珊瑚受精模型的整体弱解

摘要/Abstract

摘要：

该文致力于研究如下趋化-Navier-Stokes 珊瑚受精模型

(*)

$\left\{\begin{array}{ll}n_{t}+u \cdot \nabla n=\Delta n-\nabla \cdot\left(n f\left(|\nabla c|^{2}\right) \nabla c\right)-m n, & x \in \Omega, \\c_{t}+u \cdot \nabla c=\Delta c-c+m, & x \in \Omega, \\m_{t}+u \cdot \nabla m=\Delta m-m n, & x \in \Omega, \\u_{t}+(u \cdot \nabla) u=\Delta u-\nabla P+(n+m) \nabla \Phi, \nabla \cdot u=0, & x \in \Omega,\end{array}\right.$

其中 $\Omega \subset \mathbb{R}^3 $ 是边界光滑的有界区域, 且函数 $f\in C^{2}([0,+\infty))$ 满足

$|f(\xi)| \leq K_f \cdot (\xi + 1)^{-\frac{\theta}{2}}, \xi \geq 0,$

其中常数 $K_f > 0$ 且 $\theta \in \mathbb{R}$. 作者证明了只要

$\theta > 0,$

则对于任意适当正则的初始值与 ($*$) 相关的初边值问题在适当的齐次边界条件下有整体存在的弱解.

关键词: 趋化, 纳维-斯托克斯, 通量限制.

Abstract:

This paper is devoted to investigating the following coral fertilization model of chemotaxis-Navier-Stokes type

(*)

where $\Omega \subset \mathbb{R}^3 $ is a bounded domain with smooth boundary, and $f\in C^{2}([0,+\infty))$ fulfills

$|f(\xi)| \leq K_f \cdot (\xi + 1)^{-\frac{\theta}{2}}, \xi \geq 0,$

with constants $K_f > 0$ and $\theta \in \mathbb{R}$. It is proved that if

$\theta > 0,$

then for arbitrarily appropriately regular initial data an initial-boundary value problem associated with ($*$) subject to suitably homogeneous boundary conditions admits at least one global weak solution.

Key words: chemotaxis, Navier-Stokes, flux limitation.

中图分类号:

O175.29

崔博洋, 刘吉. 带有通量限制机制的三维趋化-Navier-Stokes 珊瑚受精模型的整体弱解[J]. 数学物理学报, 2026, 46(3): 1054-1082.

Boyang Cui, Ji Liu. Global Weak Solutions in a Three-Dimensional Coral Fertilization Model of Chemotaxis-Navier-Stokes Type with Flux Limitation[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1054-1082.

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