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

Lagrangian formulation for perfect fluid equations which hold invariant under the $\mathrm{\ell }$-conformal Galilei group with half-integer $\mathrm{\ell }$ is proposed. It is based on a Clebsch-type parametrization and reproduces Lagrangian description of the Euler fluid equations for $\mathrm{\ell }=\frac{1}{2}$. The transition from the Lagrangian formulation to the Hamiltonian one is analyzed in detail.