Cauchy Problem for Cylinder-like Capillary Jets

TL;DR

This paper extends the mathematical understanding of liquid jet motion by proving local well-posedness results for more general, non-axisymmetric jets, broadening the scope of previous axisymmetric analyses.

Contribution

It generalizes the local well-posedness results for liquid jets from axisymmetric to non-axisymmetric cases in Sobolev spaces.

Findings

Established local well-posedness for general liquid jets.

Extended mathematical framework beyond axisymmetric assumptions.

Contributed to rigorous analysis of capillary jet dynamics.

Abstract

The motion of liquid jets plays an important role in physics and engineering, and needs rigorous mathematical investigations. Recently, Huang-Karakhanyan proved the first local well-posedness in Sobolev spaces for axisymmetric jets. In this paper, we will extend this result to general jets, namely without any axisymmetry condition.