Global well-posedness of the 3D Cahn-Hilliard equations
Analysis of PDEs
2019-04-15 v1
Abstract
The Cauchy problem of the Cahn-Hilliard equations is studied in three-dimensional space. Firstly, we construct its approximate fourth-order parabolic equation, obtaining the existence of solutions by the Aubin-Lions's compactness lemma. Furthermore, we prove the uniqueness of the solution. Then, the global well-posedness is demonstrated by using energy estimates. At last, we consider a special case and get a better result about it.
Keywords
Cite
@article{arxiv.1904.06191,
title = {Global well-posedness of the 3D Cahn-Hilliard equations},
author = {Zhenbang Li and Caifeng Liu},
journal= {arXiv preprint arXiv:1904.06191},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1810.12705