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

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...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2013-01, Vol.2013 (2013), p.915-919-087
Main Authors: Li, Tailong, Xie, Jian, Chen, Ping
Format: Article
Language:English
Subjects:
Compressible fluids
Computational fluid dynamics
Entropy
Kinetic energy
Mathematical analysis
Mathematical research
Navier-Stokes equations
Self-similarity
Transport theory
Viscosity
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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 Guo and Jiang's work (2006) where the one-dimensional compressible fluids with constant viscosity are considered.
ISSN:1110-757X
1687-0042
DOI:10.1155/2013/194704