摘要
本文对无界域上非自治Navier-Stokes方程的后向紧动力学进行了研究。在时间依赖的外驱动力是弱后向缓增的假设下,证明了系统在一个能量空间上存在一个增的有界的拉回吸收集;为了克服无界域上没有紧Sobolev嵌入的困难,采用了Ball能量方程的方法证明了系统的后向渐近紧性;最后证明了无界域上非自治Navier-Stokes方程在能量空间上存在一个后向紧的拉回吸引子。
This paper is devoted to the backward-compact dynamics for a non-autonomous Navier-Stokes equation. Assume that the time-dependent force is weakly backward-tempered, then we can show that the system has an increasing and bounded pullback absorbing set in an energy space. In order to overcome the loss of compact Sobolev embedding, Ball’s method of energy equation is used to show the backward asymptotical compactness of the system. Finally, it is proved that the non-autonomous Navier-Stokes equation has a backward-compact pullback attractor in the energy space.
作者
佘连兵
高云龙
SHE Lianbing;GAO Yunlong(School of Mathematics and Information Engineering,Liupanshui Normal College,Liupanshui Guizhou 553004,China)
出处
《广西师范大学学报（自然科学版）》
CAS
北大核心
2020年第1期41-46,共6页
Journal of Guangxi Normal University:Natural Science Edition
基金
国家自然科学基金(11571283)
贵州省教育厅基金([2018]387)
六盘水师范学院项目(LPSSYKYJJ201801)
