Self-similar solutions to the isothermal compressible Navier-Stokes equations

被引：0
|
作者：
Guo, Zhenhua [1 ]
Jiang, Song
机构：
[1] Huazhong Normal Univ, Dept Math, Lab Nonlinear Analysis, Wuhan 430079, Peoples R China
[2] Inst Appl Phys & Computat Math, LCP, Beijing 100088, Peoples R China
来源：
IMA JOURNAL OF APPLIED MATHEMATICS | 2006年 / 71卷 / 05期
基金：
中国国家自然科学基金;
关键词：
self-similar solutions; isothermal compressible flows; Navier-Stokes equations;
D O I：
10.1093/imamat/hxl013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the self-similar solutions to the isothermal compressible Navier-Stokes equations. The aim of this paper is to show that there exist neither forward nor backward self-similar solutions with finite total energy. This generalizes the results for the incompressible case in Necas, J., Ruzicka, M. & Sverak, V. (1996, On Leray's self-similar solutions of the Navier-Stokes equations. Acta. Math., 176, 283-294), and is consistent with the (unproved) existence of regular solutions globally in time for the compressible Navier-Stokes equations.
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页码：658 / 669
页数：12
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