Uniqueness in a Navier–Stokes-nonlinear-Schrödinger model of superfluidity*

Abstract

Abstract In Jayanti and Trivisa (2022 J. Math. Fluid Mech. 24 46), the authors proved the existence of local-in-time weak solutions to a model of superfluidity. The system of governing equations was derived in Pitaevskii (1959 Sov. Phys. JETP 8 282–287) and couples the nonlinear Schrödinger equation and the Navier–Stokes equations. In this article, we prove a weak–strong type uniqueness theorem for these weak solutions. Only some of their regularity properties are used, allowing room for improved existence theorems in the future, with compatible uniqueness results.