Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

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

Pages: 53 – 76

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n1.a3

Authors

Bo You (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China)

Fang Li (School of Mathematics and Statistics, Xidian University, Xi’an, China)

Chang Zhang (School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, China )

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.

Keywords

global attractor, Cahn–Hilliard–Navier–Stokes system, dynamic boundary conditions, fractal dimension, the method of $\ell$-trajectories

2010 Mathematics Subject Classification

34A12, 35B40, 35Q35, 37L30

Full Text (PDF format)

This work was supported by the National Science Foundation of China Grant (11401459).

Received 23 February 2017

Accepted 1 October 2017

Published 29 March 2018