Quantum Navier–Stokes Equations

Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)

Abstract

Compressible Navier–Stokes models for quantum fluids are reviewed. They are derived from a collisional Wigner equation by a moment method and a Chapman–Enskog expansion around the quantum equilibrium. Introducing a new velocity variable, the barotropic quantum Navier–Stokes model can be reformulated as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional. This functional provides a priori estimates which are exploited to prove the global-in-time existence of weak solutions for general initial data. Furthermore, new numerical results for the isothermal model are presented.

Keywords

Stokes System Negative Differential Resistance Tunneling Diode Global Weak Solution General Initial Data 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria
  2. 2.Department of Applied MathematicsUniversity of ZagrebZagrebCroatia

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