Communications in Mathematical Sciences
Volume 16 (2018)
Finite dimensional global attractor of the Cahn–Hilliard–Navier–Stokes system with dynamic boundary conditions
Pages: 53 – 76
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.
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
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