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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
DOI/Identification number: 10.1134/S0040577916090026
Uncontrolled keywords: Euler’s equations, Poisson bracket, Poisson vertex algebra
Subjects: Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Matteo Casati
Date Deposited: 17 Aug 2018 14:14 UTC
Last Modified: 29 May 2019 20:48 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/67930 (The current URI for this page, for reference purposes)
Casati, Matteo: https://orcid.org/0000-0002-2207-4807
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