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

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  • Tailong Li
  • Ping Chen
  • Jian Xie

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.

Suggested Citation

  • Tailong Li & Ping Chen & Jian Xie, 2013. "Self‐Similar Solutions of the Compressible Flow in One‐Space Dimension," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:194704
    DOI: 10.1155/2013/194704
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    References listed on IDEAS

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    1. Lior, Noam & Sarmiento-Darkin, Wladimir & Al-Sharqawi, Hassan S., 2006. "The exergy fields in transport processes: Their calculation and use," Energy, Elsevier, vol. 31(5), pages 553-578.
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