Existence of standing and traveling waves in quantum hydrodynamics with viscosity

Abstract

We prove existence of standing waves for two quantum hydrodynamics systems with linear and nonlinear viscosity. Moreover, global existence of traveling waves is proved for the former without restrictions on the viscosity and dispersion parameters, thanks to a suitable Lyapunov function. This is an improvement with respect to the global existence result in \cite{LMZ2020}, where it was required that the viscosity is sufficiently strong.

arXiv admin note: substantial text overlap with arXiv:2004.07222