On the Low Mach Number Limit for Quantum Navier-Stokes Equations
In this paper we investigate the low Mach number limit for the quantum Navier-Stokes system considered in the three-dimensional space. For general ill-prepared initial data of finite energy, we prove strong convergence of finite energy weak solutions towards weak solutions of incompressible Navier Stokes equations. Our approach relies on a careful dispersive analysis for the acoustic part, governed by the Bogoliubov dispersion relation. The a priori bounds given by the energy and the BD entropy then yield the strong convergence towards the incompressible dynamics.