Uniqueness in a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity
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.
Keywords
Cite
@article{arxiv.2109.14083,
title = {Uniqueness in a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity},
author = {Pranava Chaitanya Jayanti and Konstantina Trivisa},
journal= {arXiv preprint arXiv:2109.14083},
year = {2022}
}
Comments
20 pages. Major revisions from previous versions including improved estimates and the removal of assumptions (small data/low energy/short time) for uniqueness