The transient equations of viscous quantum hydrodynamics

Michael Dreher

doi:10.1002/mma.918

The transient equations of viscous quantum hydrodynamics

Michael Dreher^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 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 language	English
Pages (from-to)	391-414
Number of pages	24
Journal	Mathematical Methods in the Applied Sciences
Volume	31
Issue number	4
DOIs	https://doi.org/10.1002/mma.918
Publication status	Published - 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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10.1002/mma.918

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title = "The transient equations of viscous quantum hydrodynamics",

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.",

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author = "Michael Dreher",

year = "2008",

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doi = "10.1002/mma.918",

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T1 - The transient equations of viscous quantum hydrodynamics

AU - Dreher, Michael

PY - 2008/3/10

Y1 - 2008/3/10

N2 - 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.

AB - 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.

KW - quantum hydrodynamics

KW - existence

KW - uniqueness and persistence of solutions

KW - boundary conditions of Zaremba type

KW - nonlinear Schrodinger equations

KW - inviscid limit

KW - LINEAR EVOLUTION-EQUATIONS

KW - SCHRODINGER TYPE EQUATIONS

KW - GLOBAL EXISTENCE

KW - WELL-POSEDNESS

KW - BEHAVIOR

KW - MODEL

KW - TIME

U2 - 10.1002/mma.918

DO - 10.1002/mma.918

M3 - Article

SN - 0170-4214

VL - 31

SP - 391

EP - 414

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 4

ER -

The transient equations of viscous quantum hydrodynamics

Abstract

Keywords

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