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Asymptotic Limits for Quantum Trajectory Models

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2001

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Gamba, Irene
Jüngel, Ansgar

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The semi-classical and the inviscid limit in quantum trajectory models given by a one-dimensional steady-state hydrodynamic system for quantum fluids are rigorously performed. The model consists of the momentum equation for the particle density in a bounded domain, with prescribed current density, and the Poisson equation for the electrostatic potential. The momentum equation can be written as a dispersive third-order differential equation which may include viscous terms. It is shown that the semi-classical and inviscid limit commute for sufficiently small data (i.e. current density) corresponding to subsonic states, were the inviscid non-dispersive solution is regular. In addition, we show these limits do not commute in general. The proofs are based on a reformulation of the problem as a singular second-order elliptic system and on elliptic and W1,1 estimates.

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ISO 690GAMBA, Irene, Ansgar JÜNGEL, 2001. Asymptotic Limits for Quantum Trajectory Models
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@unpublished{Gamba2001Asymp-6412,
  year={2001},
  title={Asymptotic Limits for Quantum Trajectory Models},
  author={Gamba, Irene and Jüngel, Ansgar}
}
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