Canonical description of incompressible fluid -- Dirac brackets approach

Abstract

We present a novel canonical description of the incompressible fluid dynamics. This description uses the dynamical constraints, in our case reflecting "incompressibility" assumption, and leads to replacement of usual hydrodynamical Poisson brackets for density and velocity fields with Dirac brackets. The resulting equations are then known nonlinear, and non-local in space, equations for incompressible fluid velocity.

7 pages, latex

Cited by in corpus (2)

• Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems
• Recursive properties of Dirac and Metriplectic Dirac brackets with Applications