For the 2D free-boundary Euler equations with surface tension on a droplet, there exist arbitrarily small initial velocities such that the vorticity Hessian grows at least exponentially in time.
Exponential growth of the vorticity gradient for the euler equation on the torus
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Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions
For the 2D free-boundary Euler equations with surface tension on a droplet, there exist arbitrarily small initial velocities such that the vorticity Hessian grows at least exponentially in time.