Low Mach number limit for the Quantum-Hydrodynamics system

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 toward 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.