Existence and analyticity of solutions to fractional-in-space Cahn–Hilliard equation

For the Cauchy problem of a fractional-in-space Cahn–Hilliard equation, we show the existence of a unique global-in-time solution, analyticity and decay estimates with small initial data in Wiener space $\mathcal X_T:=\widetilde{L_T^\infty}\mathcal X_0\cap L_T^1\mathcal X_2$.