三维耦合趋化—流体模型强解的全局存在性和衰减率估计  

Global Existence and Decay Rate Estimates of Strong Solutions for the Coupled 3D-chemotaxis-fluid Model

作　　者：叶宏 YE Hong(College of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi,Xinjiang,830012,P.R.China)

机构地区：[1]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830012

出　　处：《数学进展》2024年第5期1019-1038,共20页Advances in Mathematics（China）

基　　金：新疆财经大学科研基金项目(No.2022XYB006)。

摘　　要：本文研究了三维全空间中耦合趋化一流体模型的初边值问题.在[Appl.Math.Lett.,2020,105:106332,7 pp.]得出该模型Serrin型爆破准则的基础上,我们得出初值在L~3范数或H~(1/2)范数小时强解的全局存在性.作为解的全局存在性证明过程中所得估计的副产品,得出了强解的衰减率估计.This paper is concerned with an initial-boundary value problem of the chemotaxis-fluid coupled model in three-dimensional whole space.Based on the Serrin type blow-up criterion of that model obtained in [Appl.Math.Lett.,2020,105:106332,7 pp.],the global existence of solutions under the small initial data of L^(3) norm H^(1/2) norm is obtained.As a byproduct of the estimates obtained in the process of proving the global existence of solutions,the decay rate of solutions is also justified.

关 键 词：耦合趋化—流体模型 强解 全局存在性 衰减率 

分 类 号：O175.21[理学—数学]