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

TL;DR

This paper proves the existence of a finite-dimensional global attractor for the coupled Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions, analyzing long-term behavior with polynomial nonlinearities.

Contribution

It establishes the finite dimensional global attractor for the system with dynamic boundary conditions using the -trajectories method, extending understanding of long-term dynamics.

Findings

Existence of a finite dimensional global attractor.

Applicability to systems with polynomial nonlinearities of arbitrary order.

Use of the -trajectories method for analysis.

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.