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arXiv · 1509.00254

Dispersive deformations of the Hamiltonian structure of Euler's equations

Matteo Casati
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Abstract

Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to the full algebra of vector fields. Motivated by some recent results about the deformations of Lie-Poisson brackets of vector fields, we study the dispersive deformations of the Poisson brackets of Euler's equation and show that, up to the second order, they are trivial.

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BibTeXRIS

Matteo Casati. 2015-09-01. Dispersive deformations of the Hamiltonian structure of Euler's equations. https://doi.org/10.1134/s0040577916090026

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