  Molecules at the air-water interface often form inhomogeneous layers in which
domains of different densities are separated by sharp interfaces. Complex
interfacial pattern formation may occur through the competition of short- and
long-range forces acting within the monolayer. The overdamped hydrodynamics of
such interfacial motion is treated here in a general manner that accounts for
dissipation both within the monolayer and in the subfluid. Previous results on
the linear stability of interfaces are recovered and extended, and a
formulation applicable to the nonlinear regime is developed. A simplified
dynamical law valid when dissipation in the monolayer itself is negligible is
also proposed. Throughout the analysis, special attention is paid to the
dependence of the dynamical behavior on a characteristic length scale set by
the ratio of the viscosities in the monolayer and in the subphase.
