Perfect fluid equations with N=1,2 Schrödinger supersymmetry

Superconformal extensions of the perfect fluid equations, which realize [Formula: see text] Schrödinger superalgebra, are constructed within the Hamiltonian formalism. They are built by introducing real (for [Formula: see text]) or complex (for [Formula: see text]) anticommuting field variables as superpartners for the density and velocity of a fluid. The full set of conserved charges associated with the [Formula: see text] Schrödinger superalgebra is constructed. Within the Lagrangian formalism, when the Clebsch decomposition for the velocity vector field is used, the anticommuting variables can be interpreted as potentials parameterizing fluid’s vorticity.