A new form of governing equations of fluids arising from Hamilton’s principle. (English) Zbl 1210.76009
Summary: A new form of governing equation 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 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 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 cases. Some new results are extended to the two-fluid non-dispersive case.
MSC:
| 76A02 | Foundations of fluid mechanics |
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
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