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

TL;DR

This paper proves a weak-strong type uniqueness theorem for solutions to a coupled Navier-Stokes and nonlinear Schrödinger model of superfluidity, building on prior existence results and allowing for future improvements.

Contribution

It establishes a uniqueness result for weak solutions of the Navier-Stokes-NLS superfluidity model, using minimal regularity assumptions.

Findings

Proved weak-strong uniqueness for the coupled system.

The result relies on partial regularity properties of solutions.

Provides a foundation for future existence and uniqueness studies.

Abstract

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.