We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality with a large class of non-autonomous external forces. 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 pullback -attractor for the process associated to the problem. An upper bound on the fractal dimension of the pullback attractor is also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-2-2,
author = {Cung The Anh and Dang Thanh Son},
title = {Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {129-154},
zbl = {1321.76074},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-2-2}
}
Cung The Anh; Dang Thanh Son. Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains. Annales Polonici Mathematici, Tome 113 (2015) pp. 129-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-2-2/