  Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equations
with degenerate potential is shown. The nonlocality is described by means of a
symmetric singular kernel not falling within the framework of any previous
existence theory. A convection term is also taken into account. Building upon
this novel existence result, we prove convergence of solutions for this class
of nonlocal Cahn-Hilliard equations to their local counterparts, as the
nonlocal convolution kernels approximate a Dirac delta. Eventually, we show
that, under suitable assumptions on the data, the solutions to the nonlocal
Cahn-Hilliard equations exhibit further regularity, and the nonlocal-to-local
convergence is verified in a stronger topology.
