Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2012; 49(2): 357-378

Printed March 1, 2012

https://doi.org/10.4134/JKMS.2012.49.2.357

Copyright © The Korean Mathematical Society.

The existence of global attractor for convective Cahn-Hilliard equation

Xiaopeng Zhao and Bo Liu

Jilin University, Jilin University

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 $H^k$ $(k\geq0)$ space, which attracts any bounded subset of $H^k(\Omega)$ in the $H^k$-norm.

Keywords: attractor, convective Cahn-Hilliard equation, absorbing set

MSC numbers: 35B41, 35K35

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