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

Cung The Anh;  Dang Thanh Son — 2015

Annales Polonici Mathematici

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...

Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains

Cung The Anh;  Dang Thanh Son — 2014

Bulletin of the Polish Academy of Sciences. Mathematics

We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove the existence of a unique minimal finite-dimensional pullback D σ -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms.

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