摘要：本文研究了具有多孔介質(zhì)細(xì)胞擴(kuò)散和矩陣敏感性的趨化-流體耦合模型的初邊值問(wèn)題弱解的全局有界性. 在二維有界區(qū)域上， 本文首先構(gòu)造了問(wèn)題對(duì)應(yīng)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(jì)建立了解的有界性，最后對(duì)正則化系統(tǒng)取極限得到了原問(wèn)題弱解的整體存在性.所得結(jié)果推廣了 Tao 和 Winkler 的相應(yīng)結(jié)果.

關(guān)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(lèi)號(hào)： ?O175.29???文獻(xiàn)標(biāo)識(shí)碼：A???DOI：10.19907/j.0490-6756.2023.051003

收稿日期： ?2022-10-09

基金項(xiàng)目： ?四川省應(yīng)用基礎(chǔ)研究計(jì)劃項(xiàng)目（2020YJ0264）

作者簡(jiǎn)介： ??何肖肖（1998-）， 女， 四川南充人， 碩士研究生， 主要研究領(lǐng)域?yàn)槠⒎址匠? 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