Degenerate pullback attractors for the 3D Navier-Stokes equations
Analysis of PDEs
2015-09-30 v3
Abstract
As in our previous paper, the 3D Navier-Stokes equations with a translationally bounded force contain pullback attractors 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 constant is small enough, the pullback attractor will be 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.
Keywords
Cite
@article{arxiv.1403.6200,
title = {Degenerate pullback attractors for the 3D Navier-Stokes equations},
author = {Alexey Cheskidov and Landon Kavlie},
journal= {arXiv preprint arXiv:1403.6200},
year = {2015}
}