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Pullback attractors for the non-autonomous 2D Navier -- stokes equations for minimally regular forcing
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Robinson, James C., Real, Jose, Marín-Rubio, Pedro and García-Luengo, Julia (2014) Pullback attractors for the non-autonomous 2D Navier -- stokes equations for minimally regular forcing. Discrete and Continuous Dynamical Systems, Volume 34 (Number 1). pp. 203-227. doi:10.3934/dcds.2014.34.203 ISSN 1078-0947.
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Official URL: http://dx.doi.org/10.3934/dcds.2014.34.203
Abstract
This paper treats the existence of pullback attractors for the non-autonomous 2D Navier-Stokes equations in two different spaces, namely L-2 and H-1. The non-autonomous forcing term is taken in L-loc(2)(R; H-1) and L-loc(2)(R; L-2) respectively for these two results: even in the autonomous case it is not straightforward to show the required asymptotic compactness of the flow with this regularity of the forcing term. Here we prove the asymptotic compactness of the corresponding processes by verifying the flattening property - also known as "Condition (C)". We also show, using the semigroup method, that a little additional regularity - f is an element of L-loc(p)(R; H-1) or f is an element of L-loc(p)(R; L-2) for some p > 2 - is enough to ensure the existence of a compact pullback absorbing family (not only asymptotic compactness). Even in the autonomous case the existence of a compact absorbing set for this model is new when f has such limited regularity.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Discrete and Continuous Dynamical Systems | ||||||||
Publisher: | American Institute of Mathematical Sciences | ||||||||
ISSN: | 1078-0947 | ||||||||
Official Date: | January 2014 | ||||||||
Dates: |
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Volume: | Volume 34 | ||||||||
Number: | Number 1 | ||||||||
Page Range: | pp. 203-227 | ||||||||
DOI: | 10.3934/dcds.2014.34.203 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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