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 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.Comment: To appear in Research in the Mathematical Science

Abstract stability theory and applications to hyperbolic equations with time dependent dissipative force fields

AbstractIn this paper an abstract theorem of asymptotic stability, using the theory of one parameter Liapunov functions, is provided. The advantage of this approach is to remove, in several important cases, the request of precompactness of the orbits. Applications are made to an abstract class of hyperbolic equations, with time dependent dissipations, including damped and strongly damped wave equations and the extensible beam equation. The final example provides the asymptotic stability of the periodic solution to the membrane equation with a time dependent damping term