The transient equations of viscous quantum hydrodynamics

DOI10.1002/mma.918zbMath1142.35070OpenAlexW2012535684MaRDI QIDQ5448596

Michael Dreher

Publication date: 7 March 2008

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.918

zbMATH Keywords

existenceuniquenessnonlinear Schrödinger equationsquantum hydrodynamicsinviscid limitboundary conditions of Zaremba typepersistence of solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum hydrodynamics and relativistic hydrodynamics (76Y05)

Related Items (10)

The full viscous quantum hydrodynamic system in one dimensional space ⋮ Viscous quantum hydrodynamics and parameter-elliptic systems ⋮ Existence of solutions for a viscous hybrid quantum system for arbitrary large current density ⋮ Quantum Semiconductor Models ⋮ Global existence of the three-dimensional viscous quantum magnetohydrodynamic model ⋮ Asymptotic stability of the rarefaction wave for the compressible quantum Navier-Stokes-Poisson equations ⋮ Stability of a one-dimensional full viscous quantum hydrodynamic system ⋮ On the blowing up of solutions to one-dimensional quantum Navier-Stokes equations ⋮ Large data solutions to the viscous quantum hydrodynamic model with barrier potential ⋮ Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations

Cites Work

• Unnamed Item
• Global existence of small solutions to nonlinear evolution equations
• Quasi-hydrodynamic semiconductor equations
• Linear elliptic differential systems and eigenvalue problems

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