  We give a detailed study of the infinite-energy solutions of the
Cahn-Hilliard equation in the 3D cylindrical domains in uniformly local phase
space. In particular, we establish the well-posedness and dissipativity for the
case of regular potentials of arbitrary polynomial growth as well as for the
case of sufficiently strong singular potentials. For these cases, we prove the
further regularity of solutions and the existence of a global attractor. For
the cases where we have failed to prove the uniqueness (e.g., for the
logarithmic potentials), we establish the existence of the trajectory attractor
and study its properties.
