On the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions
Fang Li, Bo You · Discrete and Continuous Dynamical Systems - B · 2021
The objective of this paper is to study the fractal dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions. Inspired by the idea of the \begin{document}$ \ell $\end{document} -trajectory method, we prove the existence of a finite dimensional global attractor in an auxiliary normed space for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions and estimate the fractal dimension of the global attractor in the original phase space for this system by defining a Lipschitz mapping from the auxiliary normed space into the original phase space.