# 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…

## One Citation

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

- Mathematics, Physics
- 2021

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…

## References

SHOWING 1-10 OF 75 REFERENCES

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

- Mathematics, Physics
- 2021

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…

Global Weak Solutions to the Compressible Quantum Navier-Stokes Equations with Damping

- Physics, MathematicsSIAM J. Math. Anal.
- 2016

The existence of global weak solutions of the compressible quantum Navier--Stokes equations with large data in three dimensions (3D) is proved by using the Faedo--Galerkin method and the compactness arguments.

Global Weak Solutions to Compressible Navier-Stokes Equations for Quantum Fluids

- Mathematics, Computer ScienceSIAM J. Math. Anal.
- 2010

The main idea of the existence analysis is to reformulate the quantum Navier–Stokes equations by means of a so-called effective velocity involving a density gradient, leading to a viscous quantum Euler system.

On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics

- Mathematics, Physics
- 2008

In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models,…

Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems

- Mathematics
- 2014

We consider a general Euler-Korteweg-Poisson system in R 3, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics…

FINITE ENERGY GLOBAL SOLUTIONS TO A TWO-FLUID MODEL ARISING IN SUPERFLUIDITY

- 2015

In this paper we study a hydrodynamic system describing two interacting fluids, which can be seen as a toy model to start an investigation on the so called two-fluid models arising in superfluidity…

Local existence of solutions to the transient quantum hydrodynamic equations

- Mathematics
- 2002

The existence of weak solutions locally in time to the quantum hydrodynamic equations in bounded domains is shown. These Madelung-type equations consist of the Euler equations, including the quantum…

Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids

- Mathematics
- 2003

Abstract This paper analyzes an initial/boundary value problem for a system of equations modelling the nonstationary flow of a nonhomogeneous incompressible asymmetric (polar) fluid. Under conditions…

Strong Solutions of the Navier–Stokes Equations for Nonhomogeneous Incompressible Fluids

- Mathematics
- 2003

Abstract We study strong solutions of the Navier–Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R 3. Deriving higher a priori estimates independent of the lower bounds of the…

A Blow-Up Criterion of Strong Solutions to the Quantum Hydrodynamic Model

- Physics
- 2020

In this article, we focus on the short time strong solution to a compressible quantum hydrodynamic model. We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic…