Open Access
2013 Self-Similar Solutions of the Compressible Flow in One-Space Dimension
Tailong Li, Ping Chen, Jian Xie
J. Appl. Math. 2013: 1-5 (2013). DOI: 10.1155/2013/194704


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.


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Tailong Li. Ping Chen. Jian Xie. "Self-Similar Solutions of the Compressible Flow in One-Space Dimension." J. Appl. Math. 2013 1 - 5, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950550
MathSciNet: MR3122129
Digital Object Identifier: 10.1155/2013/194704

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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