Casati, Matteo (2016) Dispersive deformations of the Hamiltonian structure of Euler’s equations. Theoretical and Mathematical Physics, 188 (3). pp. 12961304. ISSN 00405779. (doi:10.1134/S0040577916090026) (KAR id:67930)
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Official URL https://doi.org/10.1134/S0040577916090026 
Abstract
Euler’s equations for a twodimensional fluid can be written in the Hamiltonian form, where the Poisson bracket is the Lie–Poisson bracket associated with the Lie algebra of divergencefree vector fields. For the twodimensional 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/0000000222074807 
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