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Acceleration Wave, K-Condition, and Global Existence in ET6

In: Rational Extended Thermodynamics beyond the Monatomic Gas

Author

Listed:
  • Tommaso Ruggeri

    (University of Bologna, Dept. of Mathematics and Res. Center of Applied Mathematics AM²)

  • Masaru Sugiyama

    (Nagoya Institute of Technology, Graduate School of Engineering)

Abstract

We verify the K-condition for the non-linear ET6 model and show for any gas the existence of global smooth solutions provided that initial data are sufficiently small. As an example, in the case of polyatomic gases, we study acceleration waves. We evaluate the Bernoulli equation for the amplitude of the wave. If the initial amplitude of an acceleration wave is sufficiently small compared with the critical amplitude, the acceleration wave exists for all time and decays to zero as the time t becomes large. Vice versa, for large initial amplitude, there exists a critical time at which we have the blow up of the solution and the formation of a shock wave. We show the peculiarity of this model, that is, the velocity of a disturbance and the critical time are universal: these are independent of the degrees of freedom of the constituent molecule D.

Suggested Citation

  • Tommaso Ruggeri & Masaru Sugiyama, 2015. "Acceleration Wave, K-Condition, and Global Existence in ET6," Springer Books, in: Rational Extended Thermodynamics beyond the Monatomic Gas, edition 1, chapter 0, pages 293-298, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13341-6_14
    DOI: 10.1007/978-3-319-13341-6_14
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