Self-similar solutions of the compressible flow in one-space dimension
type: Item
instance of: scholarly article
title: Self-similar solutions of the compressible flow in one-space dimension
zbMATH Open document ID: 1397.35174
DOI: 10.1155/2013/194704
author: Tailong Li
author: Ping Chen
author: Jian Xie
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: For the isentropic compressible fluids in one-space dimension, we prove that the Navier-Stokes equations with density-dependent viscosity have neither forward nor backward self-similar strong solutions with finite kinetic energy. Moreover, we obtain the same result for the nonisentropic compressible gas flow, that is, for the fluid dynamics of the Navier-Stokes equations coupled with a transport equation of entropy. These results generalize those in \textit{Z. Guo} and \textit{S. Jiang}'s work [IMA J. Appl. Math. 71, No. 5, 658--669 (2006; Zbl 1112.76059)] where the one-dimensional compressible fluids with constant viscosity are considered.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35C06
Mathematics Subject Classification ID: 76N99
Mathematics Subject Classification ID: 35D35
zbMATH DE Number: 6950550
Wikidata QID: Q59002050
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/194704
OpenAlex ID: W2036009151
DBLP publication ID: journals/jam/LiCX13
description: scientific article; zbMATH DE number 6950550