  The Cahn-Hilliard equation with degenerate mobility is used in several areas
including the modeling of living tissues. We are interested in quantifying the
pressure jump at the interface in the case of incompressible flows. To do so,
we include an external force and consider stationary radial solutions. This
allows us to compute the pressure jump in the small dispersion regime. We also
characterize compactly supported stationary solutions in the incompressible
case, prove the incompressible limit and prove convergence of the parabolic
problems to stationary states.
