二维Keller-Segel-Stokes系统的稳定性分析  

The stability analysis of a two-dimensional Keller-Segel-Stokes system

作　　者：徐艳 XU Yan(School of Mathematical Sciences,Chongqing Normal University,Chongqing,401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《内江师范学院学报》2023年第6期44-49,共6页Journal of Neijiang Normal University

基　　金：重庆市科技局面上项目(sctc2020jcyj-msxmX0560)。

摘　　要：在一个具有光滑边界的有界区域Ω■R^(2)中,研究一类不可压缩的Keller-Segel-Stokes方程组的齐次Neumann-Neumann-Dirichlet初边值问题时,其经典解的全局存在性和有界性已经在初值n_(0)的适当小性条件下建立.在此基础上进一步研究了该全局经典解的长时间行为.证明了在初值n_(0)的额外小性条件下,当时间t趋于无穷时,该全局经典解以指数的速率收敛到稳态解(n_(0),n_(0),0),其中n_(0)表示n在区域Ω上的积分平均.In a bounded domain of Ω■R^(2) with smooth boundary,the homogeneous Neumann-Neumann-Dirichlet initial-boundary-value problem of a class of uncompressible Keller-Segel-Stokes equations system has been studied,and the global existence and boundedness of the classical solutions to this problem have been constructed under the appropriate smallness condition on the initial value of n 0.Thus what's next is to study the long-time behavior of the classical solutions based on the condition above,it is proven that the classical solutions to the problem converge to the spatial equilibrium at exponential rate as t goes to infinity under the extra smallness assumption on the initial data n_(0),where the n_(0) stands for the integral mean value of n over Ω,and the gravitational potentialφbelongs to W^(2,∞)(Ω).

关 键 词：趋化 Keller-Segel-Stokes系统 渐进行为 收敛速率 

分 类 号：O175.21[理学—数学]