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