THE VISCOUS MODEL OF QUANTUM HYDRODYNAMICS IN SEVERAL DIMENSIONS

DOI10.1142/S0218202507002200zbMath1144.35012MaRDI QIDQ5386900

Li Chen, Michael Dreher

Publication date: 14 May 2008

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

zbMATH Keywords

periodic boundary conditionsexponential decaylocal and global existenceentropy dissipation method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) PDEs in connection with quantum mechanics (35Q40) Quantum hydrodynamics and relativistic hydrodynamics (76Y05)

Related Items (24)

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 ⋮ Quantum Navier–Stokes Equations ⋮ Asymptotic stability of the rarefaction wave for the compressible quantum Navier-Stokes-Poisson equations ⋮ Global existence of weak solution for quantum Navier-Stokes-Poisson equations ⋮ Initial time layer problem for quantum drift-diffusion model ⋮ Resolvent estimates for Douglis-Nirenberg systems ⋮ Existence of global weak solution for quantum Navier–Stokes system ⋮ Stability of a one-dimensional full viscous quantum hydrodynamic system ⋮ On the blowing up of solutions to one-dimensional quantum Navier-Stokes equations ⋮ The Dirichlet problem of the quantum drift-diffusion model ⋮ Existence of the solution for the viscous bipolar quantum hydrodynamic model ⋮ Large data solutions to the viscous quantum hydrodynamic model with barrier potential ⋮ Existence of global weak solutions for Navier-Stokes-Poisson equations with quantum effect and convergence to incompressible Navier-Stokes equations ⋮ The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential ⋮ Existence, semiclassical limit and long-time behavior of weak solution to quantum drift-diffusion model ⋮ Quasineutral limit of the viscous quantum hydrodynamic model for semiconductors ⋮ The bipolar quantum drift-diffusion model ⋮ Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations ⋮ AN INEQUALITY BY GIANAZZA, SAVARÉ AND TOSCANI AND ITS APPLICATIONS TO THE VISCOUS QUANTUM EULER MODEL ⋮ Asymptotic stability of the stationary wave for the quantum Navier-Stokes-Poisson system ⋮ Convergence of the quantum Navier-Stokes-Poisson equations to the incompressible Euler equations for general initial data

Cites Work

• Theory of function spaces II
• Path integral approach to quantum Brownian motion
• Compact sets in the space \(L^ p(0,T;B)\)
• Exponential decay in time of solutions of the viscous quantum hydrodynamic equations
• Fokker-Planck equations as scaling limits of reversible quantum systems
• Quantum energy-transport and drift-diffusion models
• A Positivity-Preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
• The Quantum Hydrodynamic Model for Semiconductor Devices
• On a steady-state quantum hydrodynamic model for semiconductors
• CONSERVATIVE AND NON-CONSERVATIVE BOLTZMANN-TYPE MODELS OF SEMICONDUCTOR THEORY
• A derivation of the isothermal quantum hydrodynamic equations using entropy minimization
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

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