Affiliation:
1. College of Sciences, Northeastern University, Shenyang 110004, China. E-mail: zhaoxiaopeng@mail.neu.edu.cn
Abstract
We study the well-posedness and asymptotic behavior of solutions to the Cauchy problem of a three-dimensional sixth-order Cahn–Hilliard equation arising in oil-water-surfactant mixtures. First, by using the pure energy method and a standard continuity argument, we prove that there exists a unique global strong solution provided that the H 2 -norm of the initial data is sufficiently small. Moreover, we establish suitable negative Sobolev norm estimates and obtain the optimal decay rates of the higher-order spatial derivatives of the strong solution.
Reference27 articles.
1. An L ∞ bound for solutions of the Cahn–Hilliard equation;Caffarelli;Arch. Ration. Mech. Anal.,1995
2. On the Cahn–Hilliard equation in H 1 ( R N );Cholewa;J. Differential Equations,2012
3. Dynamics of fluctuations and spinodal decomposition in polymer blends;de Gennes;J. Chem. Phys.,1980
4. Analysis of the viscous Cahn–Hilliard equation in R N;Dlotko;J. Differential Equations,2012
5. Dynamics of the modified viscous Cahn–Hilliard equation in R N;Dlotko;Topol. Methods Nonlinear Anal.,2010
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