Regularity of global attractor for a 3D magnetohydrodynamic-$\alpha $ model
Volume 120 / 2017
Annales Polonici Mathematici 120 (2017), 97-114 MSC: Primary 76W05; Secondary 35B41, 35B65. DOI: 10.4064/ap170505-18-10 Published online: 1 December 2017
We consider a 3D magnetohydrodynamic-$\alpha $ (MHD-$\alpha $ for short) model with periodic boundary conditions. Under suitable assumptions on the external force, we prove both Sobolev regularity and Gevrey regularity of the compact global attractor for the continuous semigroup associated to this model.