Existence of standing and traveling waves in quantum hydrodynamics with viscosity

2022/02/15 by Delyan Zhelyazov, Zhelyazov, Delyan
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2202.07573

openalex publication_date 2022/02/15 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

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 \citeLMZ2020, where it was required that the viscosity is sufficiently strong.

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