The nonlocal Cahn-Hilliard equation with singular potential: Well-posedness, regularity and strict separation property

We consider the nonlocal Cahn-Hilliard equation with singular potential and constant mobility. Well-posedness and regularity of weak solutions are studied. Then we establish the validity of the strict separation property in dimension two. Further regularity results as well as the existence of regular finite dimensional attractors and the convergence of a weak solution to a single equilibrium are also provided. Finally, regularity results and the strict separation property are also proven for the two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes system with singular potential.