PULLBACK V-ATTRACTOR OF A THREE DIMENSIONAL GLOBALLY MODIFIED TWO-PHASE FLOW MODEL

The existence and final fractal dimension of a pullback attractor in the space V for a three dimensional system of a non-autonomous globally modified two phase flow on a bounded domain is established under appropriate properties on the time depending forcing term. The model consists of the globally modified Navier-Stokes equations proposed in [6] for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter. The existence of the pullback attractors is obtained using the flattening property. Furthermore, we prove that the fractal dimension in V of the pullback attractor is finite.