趋化NS系统弱解的全局存在性（英文）

The Global Existence of Weak Solution to Coupled Chemotaxis NS System

本文主要研究趋化NS系统在2维的有界光滑领域Ω?R^2中.本文利用Galerkin方法证明了不可压缩的NS系统弱解的存在性.其次,利用一系列检验程序,证明了带有初边值条件的趋化NS系统弱解的局部存在性,进一步得到该系统弱解的全局存在性.

In this paper, the chemotaxis NS system is considered in two-dimensional bounded domain Ω∈ R^2 with smooth boundary. It proves the existence of weak solution of the incompressible NS system by using Galerkin method in two-dimensional. Moreover,it obtains that the system with given initial data and the corresponding initial-boundary value problem possesses a global weak solution by combining standard testing procedures with regularity estimate.