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Published in:
2015 | OriginalPaper | Chapter
14. Acceleration Wave, K-Condition, and Global Existence in ET6
Authors : Tommaso Ruggeri, Masaru Sugiyama
Published in: Rational Extended Thermodynamics beyond the Monatomic Gas
Publisher: Springer International Publishing
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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.