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

Abstract: Lagrangian formulation for perfect fluid equations which hold invariant under the $\ell$-conformal Galilei group with half-integer $\ell$ is proposed. It is based on a Clebsch-type parametrization and reproduces Lagrangian description of the Euler fluid equations for $\ell=\frac12$. The transition from the Lagrangian formulation to the Hamiltonian one is analyzed in detail.