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The transient equations of viscous quantum hydrodynamics
Author(s) -
Dreher Michael
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.918
Subject(s) - inviscid flow , mathematics , uniqueness , regularization (linguistics) , bounded function , domain (mathematical analysis) , quantum , partial differential equation , nonlinear system , mathematical analysis , space (punctuation) , quantum hydrodynamics , limit (mathematics) , dimension (graph theory) , mathematical physics , classical mechanics , physics , quantum mechanics , pure mathematics , linguistics , philosophy , artificial intelligence , computer science
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 Schrödinger type, and we prove the inviscid limit. Copyright © 2007 John Wiley & Sons, Ltd.