  The aim of this paper is to show time-decay estimates of solutions to
linearized two-phase Navier-Stokes equations with surface tension and gravity.
The original two-phase Navier-Stokes equations describe the two-phase
incompressible viscous flow with a sharp interface that is close to the
hyperplane $x_N=0$ in the $N$-dimensional Euclidean space, $N \geq 2$. It is
well-known that the Rayleigh-Taylor instability occurs when the upper fluid is
heavier than the lower one, while this paper assumes that the lower fluid is
heavier than the upper one and proves time-decay estimates of $L_p-L_q$ type
for the linearized equations. Our approach is based on solution formulas, given
by Shibata and Shimizu (2011), for a resolvent problem associated with the
linearized equations.
