The transient equations of viscous quantum hydrodynamics

Michael Dreher

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We study the viscous model of quantum hydrodynamics in a bounded domain of space dimension 1, 2, or 3, and in the full one-dimensional space. This model is a mixed-order partial differential system with nonlocal and nonlinear terms for the particle density, current density, and electric potential. By a viscous regularization approach, we show existence and uniqueness of local in time solutions. We propose a reformulation as an equation of Schrodinger type, and we prove the inviscid limit. Copyright (c) 2007 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)391-414
Number of pages24
JournalMathematical Methods in the Applied Sciences
Volume31
Issue number4
DOIs
Publication statusPublished - 10 Mar 2008

Keywords

  • quantum hydrodynamics
  • existence
  • uniqueness and persistence of solutions
  • boundary conditions of Zaremba type
  • nonlinear Schrodinger equations
  • inviscid limit
  • LINEAR EVOLUTION-EQUATIONS
  • SCHRODINGER TYPE EQUATIONS
  • GLOBAL EXISTENCE
  • WELL-POSEDNESS
  • BEHAVIOR
  • MODEL
  • TIME

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