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

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_\sigma $-attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms.