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arXiv · 0801.2333

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

Sergey Gavrilyuk·Henri Gouin
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Abstract

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.

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Sergey Gavrilyuk, Henri Gouin. 2008-01-15. A new form of governing equations of fluids arising from Hamilton's principle. https://doi.org/10.1016/s0020-7225(98)00131-1

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