Semigroups of set-valued maps and the equations of the atmosphere

From the point of view of longterm dynamics, we study multivalued and
single-valued semigroups of operators acting on complete metric
spaces. We provide necessary
and sufficient conditions for the existence of the global attractor under minimal
requirements in terms of continuity of the semigroup. As
an application, we consider the multivalued semigroup generated by the
equation ruling
the evolution of the specific humidity in a system of moist air, and we
prove the existence
of a regular global attractor.