## Journal of Applied Mathematics

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

#### Abstract

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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 194704, 5 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808177

Digital Object Identifier
doi:10.1155/2013/194704

Mathematical Reviews number (MathSciNet)
MR3122129

Zentralblatt MATH identifier
06950550

#### Citation

Li, Tailong; Chen, Ping; Xie, Jian. Self-Similar Solutions of the Compressible Flow in One-Space Dimension. J. Appl. Math. 2013 (2013), Article ID 194704, 5 pages. doi:10.1155/2013/194704. https://projecteuclid.org/euclid.jam/1394808177

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