The transient equations of viscous quantum hydrodynamics

被引：15

作者：

Dreher, Michael ^{[1
]}

机构：

[1] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2008年 / 31卷 / 04期

关键词：

quantum hydrodynamics; existence; uniqueness and persistence of solutions; boundary conditions of Zaremba type; nonlinear Schrodinger equations; inviscid limit;

D O I：

10.1002/mma.918

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：391 / 414

页数：24

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