On a linearized problem arising in the Navier–Stokes flow of a free liquid jet

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.