TY - JOUR
T1 - Dispersive deformations of the Hamiltonian structure of Euler's equations
Y1 - 2015
A1 - Matteo Casati
AB - 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.
U1 - 34700
U2 - Mathematics
U4 - 1
U5 - MAT/07
ER -