The Well-posedness of Cylindrical Jets with Surface Tension

Abstract

In 1879 Rayleigh \cite{Rayleigh} studied the stability of infinite cylindrical jets, inspired by the experiments of Plateau \cite{Plateau}. The principal question that Rayleigh asked is: under what circumstances the jet is stable, for small displacements. In this paper we show that the jet flow is well-posed in short time if the initial condition belongs to some Sobolev space, and the initial jet boundary remains uniformly bounded away from the axis of symmetry. This will be proved by the method of paradifferential calculus and paralinearization. The salient feature of these results is that no smallness assumption is imposed on the initial condition.