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A non-relativistic (Galilei-invariant) model of a perfect fluid coupled to asolenoidal field in arbitrary spatial dimension is considered. It contains anarbitrary parameter $\kappa$ and in the particular case of $\kappa=1$ itdescribes a perfect fluid coupled to a magnetic field. For a special value of$\kappa$, the theory admits the Schrodinger symmetry group which is consistentwith the magnetic case in two spatial dimensions only. Generalization to thecase of the l-conformal Galilei group for an arbitrary half-integer parameter lis constructed.

Perfect fluid coupled to a solenoidal field which enjoys the l-conformal Galilei symmetry