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Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities
We consider the Cahn-Hilliard equation on manifolds with conical
singularities. For appropriate initial data we show that the solution exists in
the maximal -regularity space for all times and becomes instantaneously
smooth in space and time, where the maximal -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.Comment: 26 page
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