In this paper, we investigate the effects exerted by the interplay among p-Laplacian diffusion, chemotaxis cross diffusion and the fluid dynamic mechanism on global boundedness of the solutions. The mathematical model considered herein appears as$$\begin{aligned} \left\{ \begin{array}{llllll} \rho _t+u\cdot \nabla \rho =\nabla \cdot (|\nabla \rho |^{p-2}\nabla \rho )-\nabla \cdot (\rho \nabla c)-\rho m,&{}\quad x\in \Omega ,\quad ~t>0,\\ c_t+u\cdot \nabla c=\Delta c-c+m,&{}\quad x\in \Omega ,\quad ~t>0,\\ m_t+u\cdot \nabla m=\Delta m-\rho m,&{}\quad x\in \Omega ,\quad ~t>0,\\ u_t+(u\cdot \nabla )u=\Delta u-\nabla P+(\rho +m)\nabla \phi ,&{}\quad x\in \Omega ,\quad ~t>0,\\ \nabla \cdot u=0,&{}\quad x\in \Omega ,\quad ~t>0, \end{array}\right. \end{aligned}$$where \(\Omega \subset {\mathbb {R}}^N~(N=2,3)\) is a general bounded domain with smooth boundary. It is proved that if either$$\begin{aligned} p>2 \end{aligned}$$for \(\kappa \in {\mathbb {R}},N=2\) or$$\begin{aligned} p>\frac{94}{45} \end{aligned}$$for \(\kappa =0,N=3\) is satisfied, then for each properly chosen initial data an associated initial-boundary problem admits a global weak solution which is bounded.

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趋化-（Navier-）Stokes系统的有界性以缓慢的p-Laplacian扩散模拟珊瑚的受精

在本文中，我们研究了p-Laplacian扩散，趋化性交叉扩散以及流体动力学机制之间的相互作用对溶液整体有界性的影响。这里考虑的数学模型显示为$$ \ begin {aligned} \ left \ {\ begin {array} {llllll} \ rho _t + u \ cdot \ nabla \ rho = \ nabla \ cdot（| \ nabla \ rho | ^ {p-2} \ nabla \ rho）-\ nabla \ cdot（\ rho \ nabla c）-\ rho m，＆{} \ quad x \ in \ Omega，\ quad〜t> 0，\\ c_t + u \ cdot \ nabla c = \ Delta c-c + m，＆{} \ quad x \ in \ Omega，\ quad〜t> 0，\\ m_t + u \ cdot \ nabla m = \ Delta m- \ rho m ，＆{} \ quad x \ in \ Omega，\ quad〜t> 0，\\ u_t +（u \ cdot \ nabla）u = \ Delta u- \ nabla P +（\ rho + m）\ nabla \ phi，＆ {} \ quad x \ in \ Omega，\ quad〜t> 0，\\ \ nabla \ cdot u = 0，＆{} \ quad x \ in \ Omega，\ quad〜t> 0，\ end {array} \对。\ end {aligned} $$其中\（\ Omega \ subset {\ mathbb {R}} ^ N〜（N = 2,3）\）是具有光滑边界的一般有界域。证明如果$$ \ begin {aligned} p> 2 \ end {aligned} $$ for \（\ kappa \ in {\ mathbb {R}}，N = 2 \）或$$ \ begin {aligned } p> \ frac {94} {45} \ end {aligned} $$满足\（\ kappa = 0，N = 3 \），然后对于每个正确选择的初始数据，一个相关的初始边界问题就可以接受一个全局边界有界的弱解。