@Article{AAM-37-4,
author = {Li, Bing and Wang, Fang,  and Xue, Ling,  and Yang, Kai,  and Zhao, Kun, },
title = {On the Cahn-Hilliard-Brinkman Equations in $\mathbb{R}^4$: Global Well-Posedness},
journal = {Annals of Applied Mathematics},
year = {2021},
volume = {37},
number = {4},
pages = {513--536},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {},
doi = {https://doi.org/10.4208/aam.OA-2021-0011},
url = {https://global-sci.com/article/72652/on-the-cahn-hilliard-brinkman-equations-in-mathbbr4-global-well-posedness}
}