• Corpus ID: 235376918

Local weak solutions to a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity

@inproceedings{Jayanti2021LocalWS,
  title={Local weak solutions to a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity},
  author={Pranava Chaitanya Jayanti and Konstantina Trivisa},
  year={2021}
}
In [Pit59], a micro-scale 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 Schrödinger 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… 
Uniqueness in a Navier-Stokes-nonlinear-Schr\"odinger model of superfluidity
In [JT21b], the authors proved the existence of local-in-time weak solutions to a model of superfluidity. The system of governing equations was derived in [Pit59] and couples the nonlinear

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