Navier-Stokes Flow for a Fluid Jet with a Free Surface

The three-dimensional Navier-Stokes flow of a viscous fluid jet bounded by a moving free surface under isothermal conditions and without surface tension is considered. The fluid domain is assumed to be periodic in the axial direction and initially axisymmetric. A local-in-time existence and regularity result is proven for the full governing equations using a contraction argument in an appropriate function space. Here a Lagrangian specification of the flow field is employedin order to mitigate the difficulties involved in dealing with an evolving fluid domain. It is also shown that the associated linear problem gives rise to an analytic semigroup of contractions on the space of divergence-free Lebesgue-square-integrable vector fields