English

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