APPLICATIONS OF THE FORMAL VARIATIONAL CALCULUS TO THE EQUATIONS OF FLUID DYNAMICS.

摘要

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.