A Class of Sixth Order Viscous Cahn-Hilliard Equation with Willmore Regularization in ? 3

Xiaopeng Zhao and Ning Duan
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Xiaopeng Zhao: College of Sciences, Northeastern University, Shenyang 110819, China
Ning Duan: College of Sciences, Northeastern University, Shenyang 110819, China

Mathematics, 2020, vol. 8, issue 11, 1-13

Abstract: The main purpose of this paper is to study the Cauchy problem of sixth order viscous Cahn–Hilliard equation with Willmore regularization. Because of the existence of the nonlinear Willmore regularization and complex structures, it is difficult to obtain the suitable a priori estimates in order to prove the well-posedness results, and the large time behavior of solutions cannot be shown using the usual Fourier splitting method. In order to overcome the above two difficulties, we borrow a fourth-order linear term and a second-order linear term from the related term, rewrite the equation in a new form, and introduce the negative Sobolev norm estimates. Subsequently, we investigate the local well-posedness, global well-posedness, and decay rate of strong solutions for the Cauchy problem of such an equation in R 3 , respectively.

Keywords: sixth order Cahn–Hilliard equation; local well-posedness; global well-posedness; decay estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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