| The Formal Variational Calculus is applied to the equations of fluid dynamics. In particular, it is shown that the equations for one-dimensional isentropic compressible flow have infinitely many higher order symmetries and a first order conservation law. The notion of a generalized fluid equation is introduced and is shown that the incompressible fluid equations inherit their Hamiltonian structure from the compressible ones. Finally, the behavior of certain Hamiltonian structures under a change in dependent variables is examined. |
