  The two-phase free boundary problem with surface tension and downforce
gravity for the Navier-Stokes system is considered in a situation where the
initial interface is close to equilibrium. The boundary symbol of this problem
admits zeros in the unstable halfplane in case the heavy fluid is on top of the
light one, which leads to the well-known Rayleigh-Taylor instability.
Instability is proved rigorously in an $L_p$-setting by means of an abstract
instability result due to Henry.
