三维趋化流体耦合系统整体解的最优衰减估计  

Optimal Decay Estimates of Global Solutions for the 3D Coupled Chemotaxis-Fluid System

作　　者：赵继红 蔡中博 罗永轲 ZHAO Jihong;CAI Zhongbo;LUO Yongke(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《数学年刊（A辑）》2022年第1期17-36,共20页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11961030);陕西省自然科学基金(No.2022JM-034);宝鸡文理学院人才引进项目(No.209040020)的资助。

摘　　要：本文主要研究一类由抛物-抛物型Keller-Segel方程组和粘性不可压Navier-Stokes方程组耦合而成的三维非线性耗散系统.利用Bony微局部分析和Besov空间插值理论,作者建立了该系统在临界Besov空间中小初值问题整体解的最优衰减估计,将[Zhao J H,Zhou J J.Temporal decay in negative Besov spaces for the 3D coupled chemotaxis-fluid equations [J].Nonlinear Analysis:Real World Applications,2018,42:160-179.]中的衰减结果的可积性指标推广至了更一般的情形.In this paper,the authors are concerned with a nonlinear dissipative system coupling the parabolic-parabolic Keller-Segel system to the viscous incompressible NavierStokes equations in spatial dimensions three.The decay estimates of global solutions were established for small initial data in critical Besov spaces with minimal regularity indices by using the Bony’s paradifferential calculus and the interpolation inequalities in Besov spaces,which extends the integrable indices of decay results in [Zhao,J.H.and Zhou,J.J.,Temporal decay in negative Besov spaces for the 3 D coupled chemotaxis-fluid equations,Nonlinear Analysis:Real World Applications,2018,vol.42,pp.160-179.] to a more broader cases.

关 键 词：趋化流体模型 Keller-Segel方程 NAVIER-STOKES方程组 衰减 BESOV空间 

分 类 号：O175.29[理学—数学]