Rapid Time-Decay Phenomenon of the Incompressible Navier–Stokes Flow in Exterior Domains

作     者：Qing Hua ZHANG Yue Ping ZHU Qing Hua ZHANG;Yue Ping ZHU

作者机构：School of SciencesNantong UniversityNantong 226019P.R.China Department of MathematicsNantong Normal CollegeNantong 226010P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第4期

页      面：745-760页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China(Grant No.11771223)。 

主　　题：Incompressible Navier–Stokes equation exterior domain strong solution rapid time-decay phenomenon higher decay rates 

摘      要：This paper focuses on the rapid time-decay phenomenon of the 3 D incompressible NavierStokes flow in exterior domains.By using the representation of the flow in exterior domains,together with the estimates of the Gaussian kernel,the tensor kernel,and the Stokes semigroup,we prove that under the assumption∫0∞∫ΩT[u,p](y,t).νdSydt=0 for the body pressure tensor T[u,p],if u0∈L1(Ω)∩Lσ3(Ω)∩W2/5,5/4(Ω)with‖u0‖3≤ηfor some sufficiently small numberη0,then rapid time-decay phenomenon of the Navier-Stokes flow appears.If additionally|x|αu0∈Lr0(Ω)for some0α1 and 1r0(1-α/3)-1 orα=1 and r0=1,then the flow exhibits higher decay rates as t→∞.