Well-posedness and large time behavior for Cahn–Hilliard–Oono equation.

In this paper, we are concerned with the well-posedness and large time behavior of Cauchy problem for Cahn–Hilliard equation in R n ( n ∈ Z + , n ≥ 3 ). First, based on the higher-order norm estimates of solutions and the mollifier technique, we obtain the local well-posedness of strong solutions. Then, by using pure energy method, standard continuity argument together with negative Sobolev norm estimates, one proves the global well-posedness and time decay estimates provided that the H n 2 + 1 -norm of initial data is sufficiently small. [ABSTRACT FROM AUTHOR]