Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space

TL;DR

This paper establishes the global well-posedness, dissipativity, and existence of a smooth global attractor for a hyperbolic relaxation of the Cahn-Hilliard-Oono equation in three-dimensional space, utilizing Strichartz estimates.

Contribution

It proves the well-posedness and attractor existence for the hyperbolic Cahn-Hilliard-Oono equation in R^3, a significant extension in the analysis of this model.

Findings

Global well-posedness in R^3

Existence of a smooth global attractor

Utilization of Strichartz estimates for the Schrödinger equation

Abstract

We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn-Hilliard-Oono equation in the whole space R^3 with the non-linearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a smooth global attractor in the naturally defined energy space is also verified. The result is crucially based on the Strichartz estimates for the linear Scroedinger equation in R^3.