Asymptotic limits of Navier-Stokes equations with quantum effects

被引：8

作者：

Yang, Jianwei ^{[1
]}

Ju, Qiangchang ^{[2
]}

Yang, Yong-Fu ^{[3
]}

机构：

[1] North China Univ Water Resources & Elect Power, Coll Math & Informat Sci, Zhengzhou 450045, Henan Province, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[3] Hohai Univ, Dept Math, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2015年 / 66卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Incompressible limit; Semiclassical limit; Relative entropy method; Quantum Navier-Stokes equations; Incompressible Navier-Stokes equations; GLOBAL WEAK SOLUTIONS; SINGULAR LIMITS; EXISTENCE;

D O I：

10.1007/s00033-015-0554-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the combined incompressible limit and semiclassical limit of the weak solutions to the barotropic quantum Navier-Stokes equations of compressible flows. By using the relative entropy method, we show that for well-prepared initial data, the weak solutions of the compressible quantum Navier-Stokes model converge to the strong solution of the incompressible Navier-Stokes equations as long as the latter exists. Furthermore, the convergence rates are also obtained.

引用

页码：2271 / 2283

页数：13

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