OPTIMAL DECAY RATES FOR THE WEAK SOLUTIONS OF THE FLOCKING PARTICLES COUPLED WITH INCOMPRESSIBLE VISCOUS FLUID MODELS  

作　　者：Houzhi TANG Shuxing ZHANG Weiyuan ZOU 汤厚志;张树兴;邹委员

机构地区：[1]School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China [2]School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,China [3]College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,China

出　　处：《Acta Mathematica Scientia》2025年第2期659-683,共25页数学物理学报(B辑英文版)

基　　金：supported by the Anhui Provincial Natural Science Foundation(2408085QA031);the third author's work was supported by the National Natural Science Foundation of China(12001033).

摘　　要：This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.

关 键 词：Cucker-Smale model incompressible Navier-Stokes equations weak solution large-time behavior optimal decay rates 

分 类 号：O175.2[理学—数学]