Uniqueness in a NavierStokesnonlinearSchrödinger model of superfluidity
Abstract
In a previous paper [arXiv:2106.04659], the authors proved the existence of localintime weak solutions to a model of superfluidity. The system of governing equations was derived by Pitaevskii in 1959 and couples the nonlinear Schrödinger equation (NLS) and the NavierStokes equations (NSE). In this article, we prove two uniqueness theorems for these weak solutions. One of them is the classical weakstrong uniqueness based on a relative entropy method. The other result trades some regularity of the stronger solution for smallness of data and short time/low energy.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.14083
 Bibcode:
 2021arXiv210914083C
 Keywords:

 Mathematics  Analysis of PDEs;
 Condensed Matter  Other Condensed Matter;
 Mathematical Physics;
 Physics  Fluid Dynamics;
 Quantum Physics
 EPrint:
 22 pages