Global well-posedness and existence of uniform attractor for magnetohydrodynamic equations

摘要

We study the global well-posedness and existence of uniform attractor for magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity and pressure coupled with a reduced from of the Maxwell equations for the magnetic field. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the magnetic field is subject to a time-dependent Dirichlet boundary condition. We first establish the global existence of weak and strong solutions to Equations (1.1)-(1.4). And at this stage, we further derive the existence of a uniform attractor for Equations (1.1)-(1.4).