THEORETICAL RESULTS ON THE EXISTENCE,REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS:APPLICATIONS TO 3D PRIMITIVE EQUATIONS  

作　　者：王仁海 郭柏灵 黄代文 Renhai WANG;Boling GUO;Daiwen HUANG(School of Mathematical Sciences,Guizhou Normal University,Guiyang 550001,China;Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)

机构地区：[1]School of Mathematical Sciences,Guizhou Normal University,Guiyang 550001,China [2]Institute of Applied Physics and Computational Mathematics,Beijing 100088,China

出　　处：《Acta Mathematica Scientia》2023年第6期2493-2518,共26页数学物理学报（B辑英文版）

基　　金：supported by China Postdoctoral Science Foundation (2020TQ0053 and 2020M680456);the research funds of Qianshixinmiao[2022]B16,Qianjiaoji[2022]124 and Qiankehepingtairencai-YSZ[2022]022;supported by the NSFC (11731014 and 11571254);supported by the NSFC (11971067,11631008,11771183)。

摘　　要：Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.

关 键 词：3D primitive equations pullback attractors REGULARITY FATTENING stability 

分 类 号：O175[理学—数学]