Year: 2021
Author: Bing Li, Fang Wang, Ling Xue, Kai Yang, Kun Zhao
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 4 : pp. 513–536
Abstract
We study the global well-posedness of large-data solutions to the Cauchy problem of the energy critical Cahn-Hilliard-Brinkman equations in $\mathbb{R}^4$. By developing delicate energy estimates, we show that for any given initial datum in $H^5(\mathbb{R}^4)$, there exists a unique global-in-time classical solution to the Cauchy problem. As a special consequence of the result, the global well-posedness of large-data solutions to the energy critical Cahn-Hilliard equation in $\mathbb{R}^4$ follows, which has not been established since the model was first developed over 60 years ago. The proof is constructed based on extensive applications of Gagliardo-Nirenberg type interpolation inequalities, which provides a unified approach for establishing the global well-posedness of large-data solutions to the energy critical Cahn-Hilliard and Cahn-Hilliard-Brinkman equations for spatial dimension up to four.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2021-0011
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 4 : pp. 513–536
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Cahn-Hilliard-Brinkman equations energy criticality Cauchy problem classical solution global well-posedness.