Local asymptotics for nonlocal convective Cahn-Hilliard equations with W1,1 kernel and singular potential

We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in case a W^{1,1} convolution kernel under homogeneous Neumann conditions. Any type potential, possibly also double-obstacle or logarithmic type, is included. Additionally, we highlight variants extensions to setting periodic boundary conditions viscosity contributions, as well connections with general theory evolutionary convergence gradient flows.