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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, Hindawi, vol. 2013, pages 1-5, October.
    • Handle: RePEc:hin:jnljam:194704
    DOI: 10.1155/2013/194704
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    Cited by:

    1. Carlo Bianca & Marco Menale, 2022. "On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain," Mathematics, MDPI, vol. 10(9), pages 1-14, April.

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