Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains
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_\sigma $-attractor for the process associated to the problem. An upper bound on the fractal dimension of the pullback attractor is also given.