Finite energy global solutions to a two-fluid model arising in Superfluidity

In this paper we study a hydrodynamic system describing two interacting uids, which can be seen as a toy model to start an investigation on the so called two- uid models arising in super uidity and Bose-Einstein condensates at nite temperatures. We show global existence of nite energy weak solutions, by using a fractional step argument which combines the study of a Cauchy problem for an appropriate nonlinear Schrodinger equation and the polar factorisation techinque. The convergence of the sequence of approximate solutions is then proved by using the dispersive properties of the nonlinear Schrodinger equation.