Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions

Abstract

In this work, we concern ourselves with the evolution of a droplet of an ideal fluid in two dimensions, which has nontrivial bulk vorticity and is only subject to the effects of surface tension. We construct initial data with initial domain being a disk and initial velocity being arbitrarily small, such that the vorticity Hessian grows exponentially infinitely in time.