Canonical description of incompressible fluid: Dirac brackets approach

We present a novel canonical description of the incompressible fluid dynami cs. This description uses the dynamical constraints, in our case reflecting incompressibility assumption, and leads to replacement of usual hydrodynam ical Poisson brackets for density and velocity fields with Dirac brackets. The resulting equations are then known nonlinear, and nonlocal in space, eq uations for incompressible fluid velocity. (C) 1999 Elsevier Science B.V. A ll rights reserved.