A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws both for non-dispersive case (Lagrangian depends only on conserved quantities) and dispersive case (Lagrangian depends also on their derivatives). For non-dispersive case the set of conservation laws allows to rewrite the governing equations in the symmetric form of Godunov-Friedrichs-Lax. The linear stability of equilibrium states for potential motions is also studied. In particular, the dispersion relation is obtained in terms of Hermitian matrices both for non-dispersive and dispersive case. Some new results are extended to the two-fluid non-dispersive case.
@article{hal-00204738,
author = {Gavrilyuk, Sergey, and Gouin, Henri},
title = {A new form of governing equations of fluids arising from Hamilton's principle},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00204738}
}
Gavrilyuk, Sergey, ; Gouin, Henri. A new form of governing equations of fluids arising from Hamilton's principle. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00204738/