Local weak solutions to a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity
Abstract
In a 1959 paper by Pitaevskii, a macroscopic model of superfluidity was derived from first principles, to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. The model couples two of the most fundamental PDEs in mathematics: the nonlinear Schr\"odinger equation (NLS) and the Navier-Stokes equations (NSE). In this article, we show the local existence of weak solutions to this system (in a smooth bounded domain in 3D), by deriving the required a priori estimates. (We will also establish an energy inequality obeyed by the weak solutions constructed in Kim's 1987 paper for the incompressible, inhomogeneous NSE.) To the best of our knowledge, this is the first rigorous mathematical analysis of a bidirectionally coupled system of the NLS and NSE.
Keywords
Cite
@article{arxiv.2106.04659,
title = {Local weak solutions to a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity},
author = {Pranava Chaitanya Jayanti and Konstantina Trivisa},
journal= {arXiv preprint arXiv:2106.04659},
year = {2022}
}
Comments
48 pages; added some references in the Introduction section