Degenerate Pullback Attractors for the 3D Navier-Stokes Equations

被引：6

作者：

Cheskidov, Alexey ^{[1
]}

Kavlie, Landon ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Sci & Engn Off MC 249 322, Chicago, IL 60607 USA

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2015年 / 17卷 / 03期

基金：

美国国家科学基金会;

关键词：

PERIODIC SOLUTIONS; EXISTENCE; SPACE;

D O I：

10.1007/s00021-015-0214-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

As was found in Cheskidov and Kavlie (Pullback attractors for generalized evolutionary systems. DCDS-B 20(3), 749-779, 2015), the 3D Navier-Stokes equations with a translationally bounded force possesses pullback attractors A(w)(t) in a weak sense. Moreover, those attractors consist of complete bounded trajectories. In this paper, we present a sufficient condition under which the pullback attractors are degenerate. That is, if the Grashof number is small enough, each section of the pullback attractor is a single point on a unique, complete, bounded, strong solution. We then apply our results to provide a new proof of the existence of a unique, strong, periodic solution to the 3D Navier-Stokes with a small, periodic forcing term.

引用

页码：411 / 421

页数：11

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