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

Savostianov, Anton; Zelik, Sergey

Abstract

We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn–Hilliard–Oono equation in the whole space R3ℝ3 with the nonlinearity 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 Schrödinger equation in R3ℝ3.

Citation

Savostianov, A., & Zelik, S. (2016). Global well-posedness and attractors for the hyperbolic Cahn–Hilliard–Oono equation in the whole space. Mathematical Models and Methods in Applied Sciences, 26(07), Article 1357. https://doi.org/10.1142/s0218202516500329

• Journal Article Type: Article
• Acceptance Date: Feb 12, 2016
• Online Publication Date: Apr 18, 2016
• Publication Date: Apr 18, 2016
• Deposit Date: Apr 25, 2017
• Publicly Available Date: May 4, 2017
• Journal: Mathematical Models and Methods in Applied Sciences
• Print ISSN: 0218-2025
• Electronic ISSN: 1793-6314
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 07
• Article Number: 1357
• DOI: https://doi.org/10.1142/s0218202516500329
• Public URL: https://durham-repository.worktribe.com/output/1360079
• Related Public URLs: https://arxiv.org/abs/1407.5890