Lagrangean structure of hydrodynamic plasma models and conservation laws

The Lagrangean structure of hydrodynamic plasma models (the multifluid plas ma model, the Hall MHD model, and the electron MHD model) is studied. The c onservation laws for these models are derived in a general form with the he lp of Noether's theorem. Each of these models is shown to admit symmetry tr ansformations under which the energy, momentum, and angular momentum are in variant. These models also admit the relabeling symmetry, which ensures the conservation of the averaged components of the generalized momentum. For t he electron MHD equations, the symmetry group obtained is proved to be exha ustive in the class of the first-order Lie-Baucklund symmetries. It is show n that an infinite set of kinematic invariants of motion (Casimirs) can be readily singled out by the transition to the Lagrangean basis.