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

Local asymptotics for nonlocal convective Cahn-Hilliard equations with W^{1,1} kernel and singular potential