# American Institute of Mathematical Sciences

October  2016, 36(10): 5387-5400. doi: 10.3934/dcds.2016037

## On uniform in time $H^2$-regularity of the solution for the 2D Cahn-Hilliard equation

 1 College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China 2 Center for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049

Received  October 2015 Revised  March 2016 Published  July 2016

In this article, we provide the uniform $H^2$-regularity results with respect to $t$ of the solution and its time derivatives for the 2D Cahn-Hilliard equation. Based on sharp a priori estimates for the solution of problem under the assumption on the initial value, we show that the $H^2$-regularity of the solution and its first and second order time derivatives only depend on $\epsilon^{-1}$.
Citation: Xinlong Feng, Yinnian He. On uniform in time $H^2$-regularity of the solution for the 2D Cahn-Hilliard equation. Discrete & Continuous Dynamical Systems, 2016, 36 (10) : 5387-5400. doi: 10.3934/dcds.2016037
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