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.
Categories: math.AP