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

Abstract

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