(untitled) (Journal of Partial Differential Equations, 2020)
In this paper, by using the L_p-L_q-estimates, regularization property of the linear part of e^-tΔ^3 and successive approximations, we consider the existence and uniqueness of global mild solutions to the sixth-order Cahn-Hilliard equation arising in oil-water-surfactant mixtures in suitable spaces, namely C^0([0,T];W^2,N(l-1)2(Ω)) when the norm \|u_0\|_W^2,N(l-1)2(Ω) is sufficiently small.