  In this work, we analyze a Stokes problem arising in the study of the
Navier-Stokes flow of a liquid jet. The analysis is accomplished by showing
that the relevant Stokes operator accounting for a free surface gives rise to a
sectorial operator which generates an analytic semigroup of contractions.
Estimates on solutions are established using Fourier methods. The result
presented is the key ingredient in a local existence and uniqueness proof for
solutions of the full nonlinear problem.
