The Hamiltonian structure for dynamic free boundary problems

@article{Lewis1986TheHS,
  title={The Hamiltonian structure for dynamic free boundary problems},
  author={D Lewis and Jerrold E. Marsden and Richard Montgomery and Tudor S. Ratiu},
  journal={Physica D: Nonlinear Phenomena},
  year={1986},
  volume={18},
  pages={391-404}
}
  • D Lewis, J. Marsden, +1 author T. Ratiu
  • Published 1986
  • Mathematics
  • Physica D: Nonlinear Phenomena
Hamiltonian structures for 2- or 3-dimensional incompressible flows with a free boundary are determined which generalize a previous structure of Zakharov for irrotational flow. Our Poisson bracket is determined using the method of Arnold, namely reduction from canonical variables in the Lagrangian (material) description. Using this bracket, the Hamiltonian form for the equations of a liquid drop with a free boundary having surface tension is demonstrated. The structure of the bracket in terms… Expand
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