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

Xinlong  Feng; Yinnian He

doi:10.3934/dcds.2016037

Article Contents

2016, Volume 36, Issue 10: 5387-5400. Doi: 10.3934/dcds.2016037

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

Xinlong Feng^1, and
Yinnian He^2,

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

Received: October 2015

Revised: March 2016

Published: May 2017

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Abstract

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 $\epsilon^{-1}$.

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Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 35Q35, 37L, 82C26.

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