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arXiv · 1910.09409

Global well-posedness and decay of solutions to the Cauchy problem of convective Cahn-Hilliard equation

Xiaopeng Zhao
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Abstract

In this paper, we consider the global well-posedness and time-decay rates of solution to the Cauchy problem for 3D convective Cahn-Hilliard equation with double-well potential via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, the $\dot{H}^{-s}$ ($0<s\leq\frac12$) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.

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Xiaopeng Zhao. 2019-10-15. Global well-posedness and decay of solutions to the Cauchy problem of convective Cahn-Hilliard equation. https://arxiv.org/abs/1910.09409

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