Low Mach number limit for the Quantum-Hydrodynamics system

TL;DR

This paper investigates the low Mach number limit of quantum-hydrodynamics, demonstrating strong convergence to incompressible Euler solutions and analyzing oscillations and entropy in a periodic domain.

Contribution

It provides the first rigorous proof of convergence from quantum-hydrodynamics to incompressible Euler equations in the low Mach limit with ill-prepared initial data.

Findings

Strong convergence of solutions to incompressible Euler system

Detailed analysis of time oscillations

Assessment of relative entropy functional

Abstract

In this paper we deal with the low Mach number limit for the system of quantum-hydrodynamics, far from the vortex nucleation regime. More precisely, in the framework of a periodic domain and ill-prepared initial data we prove strong convergence of the solutions towards regular solutions of the incompressible Euler system. In particular we will perform a detailed analysis of the time oscillations and of the relative entropy functional related to the system.