On the formation of small-time curvature singularities in vortex sheets

26 Jun 2018

The Kelvin-Helmholtz model for the evolution of an infinitesimally thin vortex sheet in an inviscid fluid is mathematically ill-posed for general classes of initial conditions. However, if the initial data, say imposed at t=0, is in a certain class of analytic functions then the problem is well-posed for a finite time until a singularity forms, say at t=ts, on the vortex-sheet interface, e.g. as illustrated by Moore (1979). However, if the problem is analytically continued into the complex plane, then the singularity, or singularities, exist for t