Inviscid, incompressible and semiclassical limits of Quantum Navier-Stokes equation

TL;DR

This paper investigates the limits of the quantum Navier-Stokes equations under inviscid, incompressible, and semiclassical regimes, demonstrating convergence to the incompressible Euler system with explicit rates based on the Mach number.

Contribution

It provides a rigorous analysis of the quantum Navier-Stokes equations' limits, establishing convergence to the Euler system using relative entropy methods and detailed initial data analysis.

Findings

Limit solutions satisfy the incompressible Euler system.

Convergence rate is estimated in terms of the Mach number.

Analysis applies to general initial data.

Abstract

IIn the paper, we consider the inviscid, incompressible and semiclassical limits limits of the barotropic quantum Navier-Stokes equations of compressible flows in a periodic domain. We show that the limit solutions satisfy the incompressible Euler system based on the relative entropy inequality and on the detailed analysis for general initial data. The rate of convergence is estimated in terms of the Mach number.