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IHEP 2001 - 35 (In Russian) | |
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| V.O.Soloviev | ||
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Boundary Values as Hamiltonian Variables. III. Ideal Fluid with a Free Surface | ||
| Protvino, 2001.- p.24, refs.:23. | ||
An application of the approach to Hamiltonian treatment of boundary terms proposed in previous articles of this series is considered. Here the Hamiltonian formalism is constructed and the role of standard boundary conditions is revealed for a nonviscid compressible fluid with surface tension which moves in a field of the Newtonian gravitational potential. It is shown that these boundary conditions guarantee absence of singular contributions to the equations of motion, i.e. to the Hamiltonian vector fields. From the other side the Hamiltonian variation contains a nonzero boundary term. Such Hamiltonians are usually treated as ``non-differentiable'' or ``inadmissible''. We conclude that non-differentiable functionals can be admissible Hamiltonians for nonultralocal Poisson brackets. We give a four-sided picture of free surface dynamics: both in Lagrangian and in Eulerian variables and also both in variational and in Hamiltonian approaches.
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