一维稳态量子Navier-Stokes方程组分析

数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 719-727.

一维稳态量子Navier-Stokes方程组分析

董建伟¹|张又林²|王艳萍¹

1.郑州航空工业管理学院数理系郑州 450015|2.郑州航空工业管理学院图书馆郑州 450015

收稿日期:2012-06-27 修回日期:2013-04-26 出版日期:2013-08-25 发布日期:2013-08-25
基金资助:
河南省高等学校青年骨干教师计划项目(2006110016)和河南省教育厅科学技术研究重点项目(12A110024) 资助

Analysis of the Stationary Quantum Navier-Stokes Equations in one Space Dimension

DONG Jian-Wei¹, ZHANG You-Lin², WANG Yan-Ping¹

1.Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou |450015;
2.Library, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015

Received:2012-06-27 Revised:2013-04-26 Online:2013-08-25 Published:2013-08-25

摘要/Abstract

摘要：

研究一维稳态量子Navier-Stokes方程组. 在边界条件比文献[Dong J. Classical solutions to one-dimensional stationary quantum Navier-Stokes equations. J Math Pures Appl, 2011, 96: 521--526]更广义的情况下证明了其古典解的存在性. 另外, 在某些条件下研究了其解的唯一性. 证明主要是把此问题转化为一个四阶椭圆方程.

关键词: 量子Navier-Stokes方程组, 稳态解, 存在性, 唯一性

Abstract:

The steady-state quantum Navier-Stokes equations in one space dimension are studied. The existence of classical solutions is proved under the boundary conditions more generalized than that of [Dong J. Classical solutions to
one-dimensional stationary quantum Navier-Stokes equations. J Math Pures Appl, 2011, 96: 521--526]. In addition, the uniqueness of the solutions is investigated under some assumptions. The proofs are based on a reformulation of the problem as a fourth-order elliptic equation by using an exponential variable transformation.

Key words: Quantum Navier-Stokes equations, Stationary solutions, Existence, Uniqueness

中图分类号:

35J40

董建伟, 张又林, 王艳萍. 一维稳态量子Navier-Stokes方程组分析[J]. 数学物理学报, 2013, 33(4): 719-727.

DONG Jian-Wei, ZHANG You-Lin, WANG Yan-Ping. Analysis of the Stationary Quantum Navier-Stokes Equations in one Space Dimension[J]. Acta mathematica scientia,Series A, 2013, 33(4): 719-727.

参考文献

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[3] J"ungel A, Mili\v{s}i'c J P. Full compressible Navier-Stokes equations for quantum fluids: derivation and numerical solution. Kinetic and Related Models, 2011, 4(3): 785--807

[4] J"ungel A, L'opez J L, G'amez J M. A new derivation of the quantum Navier-Stokes equations in the Wigner-Fokker-Planck approach. J Stat Phys, 2011, 145: 1661--1673

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[7] J\"{u}ngel A. Effective velocity in compressible Navier-Stokes equations with third-order derivatives. Nonlin Anal, 2011, 74: 2813--2818

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