3D convective Cahn-Hilliard equation

Abstract

We consider the initial boundary value problem for the 3D convective Cahn - Hilliard equation with periodic boundary conditions. This gives rise to a continuous dynamical system on L-2(ohm). Absorbing balls in L-2(ohm), H-per(1)(ohm) and H-per(2)(ohm) are shown to exist. Combining with the compactness property of the solution semigroup we conclude the existence of the global attractor. Restricting the dynamical system on the absorbing ball in H-per(2)(ohm) and using the general framework in Eden et. all. [] the existence of an exponential attractor is guaranteed. This approach also gives an explicit upper estimate of the dimension of the exponential attractor, albeit of the global attractor.