Global well-posedness and temporal decay estimates to the fractional Cahn–Hilliard equation in ℝ N \mathbb{R}^{N}

Abstract

AbstractThis paper is devoted to study the global well-posedness of solutions for the Cauchy problem of the fractional Cahn–Hilliard equation in{\mathbb{R}^{N}}({N\in\mathbb{N}^{+}}), provided that the initial datum is sufficiently small. In addition, the{L^{p}}-norm ({1\leq p\leq\infty}) temporal decay rate for weak solutions and the higher-order derivative of solutions are also studied.