Abstract In this paper, we consider the Cauchy problem for a coupled Cahn–Hilliard system in R 3 R^3. This system can be seen as the stationary system of a novel thermodynamically consistent three-phase model. The small initial data global existence of strong solutions are proved. Moreover, the optimal decay rates of the higher-order spatial derivatives of the strong solution are established, the H ̇ − s {H}^-s 0 ≤ s 3 2 (0 s< 32) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.
Duan et al. (Thu,) studied this question.