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

Tailong Li, Ping Chen and Jian Xie

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/194704

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:194704

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