  We consider two-layers of immiscible liquids confined between an upper and a
lower rigid plate. The dynamics of the free liquid-liquid interface is
described for arbitrary amplitudes by a single evolution equation derived from
the basic hydrodynamic equations using long-wave approximation. After giving
the evolution equation in a general way, we focus on interface instabilities
driven by gravity, thermocapillary and electrostatic fields. First, we study
the linear stability discussing especially the conditions for destabilizing the
system by heating from above or below. Second, we use a variational formulation
of the evolution equation based on an energy functional to predict metastable
states and the long-time pattern morphology (holes, drops or maze structures).
Finally, fully nonlinear three-dimensional numerical integrations are performed
to study the short- and long-time evolution of the evolving patterns. Different
coarsening modes are discussed and long-time scaling exponents are extracted.
