Rigorous derivation of the hydrodynamical equations for rotating superfluids

Abstract

Using a modified WKB approach, we present a rigorous semi-classical analysis for solutions of nonlinear Schroedinger equations with rotational forcing. This yields a rigorous justification for the hydrodynamical system of rotating superfluids. In particular it is shown that global-in-time semi-classical convergence holds whenever the limiting hydrodynamical system has global smooth solutions and we also discuss the semi-classical dynamics of several physical quantities describing rotating superfluids.