摘要：本文研究了具有多孔介質(zhì)細胞擴散和矩陣敏感性的趨化-流體耦合模型的初邊值問題弱解的全局有界性. 在二維有界區(qū)域上， 本文首先構造了問題對應的正則化系統(tǒng)，建立系統(tǒng)經(jīng)典解的全局存在性，然后借助能量估計建立了解的有界性，最后對正則化系統(tǒng)取極限得到了原問題弱解的整體存在性.所得結果推廣了 Tao 和 Winkler 的相應結果.

關鍵詞：趨化Navier-Stokes系統(tǒng); 多孔介質(zhì); 矩陣敏感度; 全局有界

中圖分類號： ?O175.29???文獻標識碼：A???DOI：10.19907/j.0490-6756.2023.051003

收稿日期： ?2022-10-09

基金項目： ?四川省應用基礎研究計劃項目（2020YJ0264）

作者簡介： ??何肖肖（1998-）， 女， 四川南充人， 碩士研究生， 主要研究領域為偏微分方程. E-mail：xiao_x_he@163.com

Global boundedness of a 2D chemotaxis Navier-Stokes system ?with porous medium cell diffusion and matrix sensitivity

HE Xiao-Xiao

（School of Mathematics， UESTC， Chengdu 611731， China）

In this paper， the global boundedness of weak solutions for the initial-boundary value problem of a chemotaxis-fluid coupling model with porous medium cell diffusion and matrix sensitivity is considered. Firstly， a regularized system is constructed for the problem， and the global classical solvability of the regularized system is established. Then the boundedness of the solutions is obtained with the help of some energy estimates. Finally， the global existence of the weak solutions of the original problem is obtained by taking limit in the regularized system. The obtained results generalize the corresponding results of Tao and Winkler.

Chemotaxis-Navier-Stokes system; Porous medium cell diffusion; Matrix sensitivity; Global boundedness