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Journal of Applied Mathematics
Volume 2013, Article ID 194704, 5 pages
Research Article

Self-Similar Solutions of the Compressible Flow in One-Space Dimension

1School of Economics & Management, Zhejiang Sci-Tech University, Hangzhou 310018, China
2Shanghai Baosteel Industry Technological Service Co., Ltd., Tongji Road 3521, Baoshan Area, Shanghai 201900, China
3Department of Mathematics, Hangzhou Normal University, Hangzhou 310016, China

Received 29 July 2013; Accepted 17 September 2013

Academic Editor: Hui-Shen Shen

Copyright © 2013 Tailong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 Guo and Jiang's work (2006) where the one-dimensional compressible fluids with constant viscosity are considered.