Nonlocal nonlinear Schrodinger equations as models of superfluidity

Condensate models for superfluid helium II with nonlocal potentials are con sidered. The potentials are chosen so that the models give a good fit to th e Landau dispersion curve; ie., the plot of quasi-particle energy E versus momentum p has the correct slope at the origin (giving the correct sound ve locity) and the roton minimum is close to that experimentally observed. It is shown that for any such potential the condensate model has non-physical features, specifically the development of catastrophic singularities and un physical mass concentrations. Two numerical examples are considered: the ev olution of a radially symmetric mass disturbance and the flow around a soli d sphere moving with constant velocity, both using the nonlocal Ginsburg-Pi taevskii model. During the evolution of the solution in time, mass concentr ations develop at the origin in the radially symmetric case and along the a xis of symmetry for the motion of the sphere.