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arXiv · 1903.06628

Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities

Pedro T. P. Lopes·Nikolaos Roidos
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Abstract

We consider the Cahn-Hilliard equation on manifolds with conical singularities. For appropriate initial data, we show that the solution exists in the maximal $L^q$-regularity space for all times and becomes instantaneously smooth in space and time, where the maximal $L^q$-regularity is obtained in the sense of Mellin-Sobolev spaces. Moreover, we provide precise information concerning the asymptotic behavior of the solution close to the conical tips in terms of the local geometry.

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Pedro T. P. Lopes, Nikolaos Roidos. 2019-03-15. Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities. https://arxiv.org/abs/1903.06628

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