Global existence and large time behavior for a two-dimensional chemotaxis-Navier-Stokes system
Global existence and large time behavior for a two-dimensional chemotaxis-Navier-Stokes system
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二维趋化-纳维-斯托克斯系统的全局存在性和大时间行为
DOI：
10.1016/j.jde.2017.07.015
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发表时间：
2017
影响因子：
2.4
通讯作者：
Xiang Zhaoyin
中科院分区：
文献类型：
--
作者：
Duan Renjun;Li Xie;Xiang Zhaoyin
本文研究二维耦合趋化性-Navier-Stokes系统。在[19]中提出了这样一个系统来描述液滴中细菌悬浮液产生的集体效应。在关于参数函数χ(⋅)、k(⋅)和势函数ϕ的一些基本假设下，我们证明了柯西问题和补充了一些初值的初边值问题弱解和经典解的整体存在性。对于初边值问题，我们还证明了解在大时间内收敛到空间齐次平衡点(n0‾，0，0)，其中n0‾：=1|Ω|∫Ωn0(X)dx。我们的结果还表明，即使包含N-S流体，胞元密度或化学浓度的大扩散也可以排除有限时间爆破的可能性。
This paper concerns the coupled chemotaxis-Navier–Stokes system in the two-dimensional setting. Such a system was proposed in [19] to describe the collective effects arising in bacterial suspensions in fluid drops. Under some basic assumptions on the parameter functions χ (⋅), k (⋅) and the potential function ϕ, which are consistent with those used by the experimentalists but weaker than those appeared in the known mathematical works, we establish the global existence of weak solutions and classical solutions for both the Cauchy problem and the initial-boundary value problem supplemented with some initial data. For the initial-boundary value problem, we also assert that the solution converges in large time to the spatially homogeneous equilibrium (n 0‾, 0, 0) with n 0‾:= 1| Ω|∫ Ω n 0 (x) d x. Our results also show that the large diffusion of the cell density or the chemical concentration can rule out the finite-time blow-up even though the Navier–Stokes fluid is included.