We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent and “small”, the existence, uniqueness and global stability of a stationary solution are also studied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-3-5,
author = {Cung The Anh and Dao Trong Quyet},
title = {Long-time behavior for 2D non-autonomous g-Navier-Stokes equations},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {277-302},
zbl = {1298.35018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-3-5}
}
Cung The Anh; Dao Trong Quyet. Long-time behavior for 2D non-autonomous g-Navier-Stokes equations. Annales Polonici Mathematici, Tome 105 (2012) pp. 277-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-3-5/