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. © 2012 Elsevier Ltd.
Journal of Mathematical Analysis and Applications
Ceci, S., & Hagen, T. (2012). On a linearized problem arising in the Navier-Stokes flow of a free liquid jet. Journal of Mathematical Analysis and Applications, 395 (1), 131-143. https://doi.org/10.1016/j.jmaa.2012.05.023