Uniqueness in a Navier-Stokes-nonlinear-Schr\'odinger model of superfluidity

In a previous paper [Jayanti, P.C., Trivisa, K. Local Existence of Solutions to a Navier-Stokes-Nonlinear-Schr\"odinger Model of Superfluidity. J. Math. Fluid Mech. 24, 46 (2022)], the authors proved the existence of local-in-time weak solutions to a model of superfluidity. The system of governing equations was derived by Pitaevskii in 1959 and couples the nonlinear Schr\"odinger equation (NLS) and the Navier-Stokes equations (NSE). 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.
Comment: 20 pages. Major revisions from previous versions including improved estimates and the removal of assumptions (small data/low energy/short time) for uniqueness