Rigorous derivation of the hydrodynamical equations for rotating superfluids

TL;DR

This paper provides a rigorous semi-classical derivation of hydrodynamical equations for rotating superfluids using a modified WKB approach, establishing convergence and analyzing physical quantities involved.

Contribution

It introduces a rigorous semi-classical analysis for nonlinear Schrödinger equations with rotation, justifying hydrodynamical models of rotating superfluids.

Findings

Global-in-time semi-classical convergence under smooth solutions

Rigorous derivation of hydrodynamical equations for rotating superfluids

Analysis of semi-classical dynamics of physical quantities

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.