Inertial Manifolds for the 3D Cahn-Hilliard Equations with Periodic Boundary Conditions
Anna Kostianko, Sergey Zelik
TL;DR
This paper proves the existence and regularity of inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions, advancing the understanding of long-term dynamics in such systems.
Contribution
It extends the spatial averaging principle to establish inertial manifolds for the 3D Cahn-Hilliard equation with periodic boundaries, including their regularity.
Findings
Existence of inertial manifolds for the 3D Cahn-Hilliard equation.
Extra regularity properties of these manifolds.
Application of the spatial averaging principle to this problem.
Abstract
The existence of an inertial manifold for the 3D Cahn-Hilliard equation with periodic boundary conditions is verified using the proper extension of the so-called spatial averaging principle introduced by G. Sell and J. Mallet-Paret. Moreover, the extra regularity of this manifold is also obtained.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Stability and Controllability of Differential Equations · Solidification and crystal growth phenomena