Traveling waves for quantum hydrodynamics with nonlinear viscosity

DOI10.1016/j.jmaa.2020.124503zbMath1454.76112arXiv2004.07222OpenAlexW3077767150MaRDI QIDQ2208269

Delyan Zhelyazov, Corrado Lattanzia

Publication date: 23 October 2020

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07222

zbMATH Keywords

compressible Euler equationsBohm potentialLax shockdispersive-diffusive shock wave

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Quantum hydrodynamics and relativistic hydrodynamics (76Y05)

Related Items (6)

Existence of standing and traveling waves in quantum hydrodynamics with viscosity ⋮ Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics ⋮ Spectral stability of weak dispersive shock profiles for quantum hydrodynamics with nonlinear viscosity ⋮ Global existence of finite energy weak solutions to the quantum Navier-Stokes equations with non-trivial far-field behavior ⋮ Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity ⋮ Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity

Cites Work

• Unnamed Item
• Unnamed Item
• Quantum hydrodynamics with nonlinear interactions
• Low Mach number limit for the quantum hydrodynamics system
• Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics
• Stationary solution for transient quantum hydrodynamics with Bohmenian-type boundary conditions
• The quantum hydrodynamics system in two space dimensions
• On the finite energy weak solutions to a system in quantum fluid dynamics
• On the shock wave spectrum for isentropic gas dynamics with capillarity
• Steady states and interface transmission conditions for heterogeneous quantum-classical 1-D hydrodynamic model of semiconductor devices
• Dispersive shocks in quantum hydrodynamics with viscosity
• Global existence of finite energy weak solutions of quantum Navier-Stokes equations
• On Navier-Stokes-Korteweg and Euler-Korteweg systems: application to quantum fluids models
• Numerical investigations of dispersive shocks and spectral analysis for linearized quantum hydrodynamics
• Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems
• Quasi-Neutral Limit, Dispersion, and Oscillations for Korteweg-Type Fluids
• Traveling wave solutions for a quantum hydrodynamic model

This page was built for publication: Traveling waves for quantum hydrodynamics with nonlinear viscosity