# Dispersive deformations of the Hamiltonian structure of Euler’s equations

Casati, Matteo (2016) Dispersive deformations of the Hamiltonian structure of Euler’s equations. Theoretical and Mathematical Physics, 188 (3). pp. 1296-1304. ISSN 0040-5779. (doi:10.1134/S0040577916090026)

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https://doi.org/10.1134/S0040577916090026

## Abstract

Euler’s equations for a two-dimensional fluid can be written in the Hamiltonian form, where the Poisson bracket is the Lie–Poisson bracket associated with the Lie algebra of divergence-free vector fields. For the two-dimensional hydrodynamics of ideal fluids, we propose a derivation of the Poisson brackets using a reduction from the bracket associated with the full algebra of vector fields. Taking the results of some recent studies of the deformations of Lie–Poisson brackets of vector fields into account, we investigate the dispersive deformations of the Poisson brackets of Euler’s equation: we show that they are trivial up to the second order.

Item Type: Article 10.1134/S0040577916090026 Euler’s equations, Poisson bracket, Poisson vertex algebra Q Science > QC Physics > QC20 Mathematical Physics Faculties > Sciences > School of Mathematics Statistics and Actuarial ScienceFaculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Matteo Casati 17 Aug 2018 14:14 UTC 29 May 2019 20:48 UTC https://kar.kent.ac.uk/id/eprint/67930 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-2207-4807