Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains

Cung The Anh, and Dang Thanh Son. "Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains." Annales Polonici Mathematici 113.2 (2015): 129-154. <http://eudml.org/doc/280819>.

@article{CungTheAnh2015,
abstract = {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 $D_σ$-attractor for the process associated to the problem. An upper bound on the fractal dimension of the pullback attractor is also given.},
author = {Cung The Anh, Dang Thanh Son},
journal = {Annales Polonici Mathematici},
keywords = {2D MHD equations; unbounded domain; Poincaré inequality; pullback attractor; fractal dimension; energy equation method},
language = {eng},
number = {2},
pages = {129-154},
title = {Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains},
url = {http://eudml.org/doc/280819},
volume = {113},
year = {2015},
}

TY - JOUR
AU - Cung The Anh
AU - Dang Thanh Son
TI - Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains
JO - Annales Polonici Mathematici
PY - 2015
VL - 113
IS - 2
SP - 129
EP - 154
AB - 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 $D_σ$-attractor for the process associated to the problem. An upper bound on the fractal dimension of the pullback attractor is also given.
LA - eng
KW - 2D MHD equations; unbounded domain; Poincaré inequality; pullback attractor; fractal dimension; energy equation method
UR - http://eudml.org/doc/280819
ER -