%0 Journal Article
%T 一类具有低正则初值的趋化–流体耦合模型解的整体存在性<br>Global Existence of Solutions for a Chemotaxis-Fluid Coupling Model with Low Regular Initial Data
%A 陈娟
%A 韩永杰
%J Pure Mathematics
%P 3272-3285
%@ 2160-7605
%D 2023
%I Hans Publishing
%R 10.12677/PM.2023.1311341
%X 考虑在三维有界区域上带有logistic源的具有信号消耗机制的趋化–流体耦合方程组：<img src=\"Edit_054cf280-a555-47a9-b318-2e1d26573125.png\" alt=\"\" />的初边值问题，其中Ω？？<sup>3</sup>是一个具有光滑边界的有界区域；n和c满足齐次Neumann边界条件，u满足Dirichlet边界条件；Φ∈W<sup>2,∞</sup>(Ω)；r&gt;0，μ&gt;0，α&gt;1是给定的参数。此前的结果表明：当初值满足n<sub>0</sub>∈C<sup>0</sup>(<span style=\"text-decoration:overline;\">Ω</span>)时，该模型在三维有界凸区域上存在整体弱解。本文进一步研究了当初值条件正则性更低时，该模型弱解的整体存在性。具体而言，初值n<sub>0</sub>满足n<sub>0</sub>∈L<sup>1</sup>(Ω)，该模型在三维有界凸区域上存在整体弱解。<br />
This paper mainly studies the initial-boundary value problem of chemotaxis-fluid coupling equations <img src=\"Edit_e30f344c-1d8f-42f1-9915-6f743699a70e.png\" alt=\"\" />with signal consumption mechanism on a three-dimensional bounded domain with logistic source where Ω？？<sup>3</sup> is bounded domain with smooth boundary; n and c satisfy the homogeneous Neu-mann boundary condition and u satisfy the Dirichlet boundary condition; where Φ∈W<sup>2,∞</sup>(Ω); where r&gt;0, μ&gt;0, and α&gt;1 are given parameters. Previous results show that the initial value satisfies n<sub>0</sub>∈C<sup>0</sup>(<span style=\"text-decoration:overline;\">Ω</span>), the model has a globally weak solution on the three-dimensional bounded convex region. This paper further examines when the initial value condition regularity is lower, the globally existence of weak solutions in this model. Specifically, the initial value n<sub>0</sub> satisfies n<sub>0</sub>∈L<sup>1</sup>(Ω), the model has a global weak solution on a three-dimensional bounded convex region.
%K 趋化–流体耦合模型，Logistic源，弱解<br>Chemotaxis-Fluid Coupling Model
%K Logistic Source
%K Weak Solution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=76236