The transient equations of viscous quantum hydrodynamics | Zendy

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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.

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