Global well-posedness of the 3D Cahn-Hilliard equations

Zhenbang Li; Caifeng Liu

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arXiv · 1904.06191

Global well-posedness of the 3D Cahn-Hilliard equations

Zhenbang Li·Caifeng Liu

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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.

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Zhenbang Li, Caifeng Liu. 2019-04-11. Global well-posedness of the 3D Cahn-Hilliard equations. https://arxiv.org/abs/1904.06191

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