A new form of governing equations of fluids arising from Hamilton's principle

A new form of governing equation is derived from Hamilton's principle of le ast action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields cons ervation laws both for the non-dispersive cases (Lagrangian depends only on conserved quantities) and the dispersive cases (Lagrangian depends also on their derivatives). For the non-dispersive cases the set of conservation l aws allows to rewrite the governing equations in the symmetric form of Godu nov-Friedrichs-Lax. The linear stability of equilibrium states for potentia l motions is also studied. In particular, the dispersion relation is obtain ed in terms of Hermitian matrices both for non-dispersive and dispersive ca ses. Some new results are extended to the two-fluid non-dispersive case. (C ) 1999 Elsevier Science Ltd. All rights reserved.