  Consider the two-phase free boundary problem subject to surface tension and
gravitational forces for a class of non-Newtonian fluids with stress tensors
$T_i$ of the form $T_i=-\pi I+\mu_i(|D(v)|^2)D(v)$ for $i=1,2$, respectively,
and where the viscosity functions $\mu_i$ satisfy $\mu_i(s)\in C^3([0,\infty))$
and $\mu_i(0)>0$ for $i=1,2$. It is shown that for given $T>0$ this problem
admits a unique, strong solution on $(0,T)$ provided the initial data are
sufficiently small in their natural norms.
