Formal stability of liquid drops with surface tension

Debra Lewis, Jerrold Marsden, and Tudor Ratiu

In Perspectives in Nonlinear Dynamics, World Scientific, (M. F. Shlesinger and R. Cawley and A. W. Saenz and W. Zachary, eds.), 71-83.

Abstract:

A planar circular liquid drop with radius r, surface tenstion $\tau$ and rotating with angular frequency $\Omega$ is shown to be formally stable, in the sense of a positive definite second variation of a combination of conserved quantities, if 3$\tau$/r³ > ($\Omega$/2)². The proof is based on the energy-Casimir method and the Hamiltonian structure of dynamic free boundary problems.