Finite dimensional global attractor of the Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions

Abstract

In this paper, we mainly consider the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions and two polynomial growth nonlinearities of arbitrary order. We prove the existence of a finite dimensional global attractor for the Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions by using the $\ell$-trajectories method.