The Existence of Global Attractor for Convective Cahn-Hilliard Equation

Abstract

Abstract. In this paper, we consider the convective Cahn-Hilliard equation. Based on the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors, we prove that the convective Cahn-Hilliard equation possesses a global attractor in H k (k ≥ 0) space, which attracts any bounded subset of H k (Ω) in the H k -norm.

On global dynamics of 2D convective Cahn–Hilliard equation

“…Remark 1.4 In the previous papers [18,20,21], my cooperators and I also studied the existence of global attractor for a 2D convective Cahn-Hilliard equation. There are two main differences between the previous results and Theorem 1.3.…”

Fourier Spectral Approximation to Global Attractor for 2D Convective Cahn–Hilliard Equation

“…We now consider the Fourier spectral method for the problem (1)- (3)., the existence of a solution locally in time is proved by the standard Picard iteration, global classical existence results can be found in [12]. Adjusted to our needs, the results is given in the following form:…”

“…Zhao and Liu [8,9] considered the optimal control problem for the convective Cahn-Hilliard equation in 1D and 2D case. For more recent results on the convective Cahn-Hilliard equation, we refer the reader to [10,11,12] and the references therein.…”

Global Attractor for Coupled Two-Compartment Gray-Scott Equations

“…There are many studies on the existence of global attractors for diffusion equations. For the classical results we refer the reader to [3,11,19,21,22,24]. Recently, based on the iteration technique for regularity estimates, combining with the classical existence theorem of global attractors, Song et al [17,18] considered the global attractor for some parabolic equations, such as Cahn-Hilliard equation, Swift-Hohenberg equation and so on, in H k (0 ≤ k ≤ ∞) space.…”