On the Hamiltonian for water waves
| Autor: | Craig, Walter |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution of their solutions can be expressed in terms of a Hamiltonian vector field. It is known from the work of VE Zakharov that the equations for water waves can be posed as a Hamiltonian dynamical system, and that the equilibrium solution is an elliptic stationary point. In this article we generalize the Hamiltonian formulation of water waves by Zakharov to a general coordinatization of the dynamical free surface, which allows it to apply to situations that include overturning wave profiles. This answers a question posed to the author by T.~Nishida during the RIMS Symposium on Mathematical Analysis in Fluid and Gas Dynamics that took place during July 6 - 8 2016. Comment: 10 pages |
| Databáze: | arXiv |
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