Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry

Lagrangian formulation for perfect fluid equations which hold invariant under the -conformal Galilei group with half-integer is proposed. It is based on a Clebsch-type parametrization and reproduces Lagrangian description of the Euler fluid equations for =12. The transition from the Lagrangian formulation to the Hamiltonian one is analyzed in detail.