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

Cung The Anh¹ ; Dang Thanh Son²

¹ Department of Mathematics Hanoi University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
² Foundation Sciences Faculty Telecommunications University 101 Mai Xuan Thuong Nha Trang, Khanh Hoa, Vietnam

Annales Polonici Mathematici, Tome 113 (2015) no. 2, pp. 129-154.

Résumé

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.

Détail

DOI : 10.4064/ap113-2-2

Keywords: study magnetohydrodynamic mhd equations viscous incompressible resistive fluid system navier stokes equations velocity field coupled convection diffusion equation magnetic fields arbitrary bounded unbounded domain satisfying poincar inequality large class non autonomous external forces existence weak solution problem proved using galerkin method existence unique minimal pullback sigma attractor process associated problem upper bound fractal dimension pullback attractor given