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

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arxiv 1903.06628 v2 pith:SUVOKHAU submitted 2019-03-15 math.AP

Pedro T. P. Lopes , Nikolaos Roidos This is my paper · ORCID
classification math.AP
keywords conicalcahn-hilliardequationmanifoldsmaximalregularitysingularitiessolution
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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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  1. The fractional porous medium equation on manifolds with conical singularities I

    math.AP 2019-08 accept novelty 6.0 of 10

    The paper proves short-time existence, uniqueness and maximal L^q-regularity for the fractional porous medium equation on manifolds with conical singularities, and gives the decay rate of solutions near the conical tips.

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