Non-Linear Maximum Entropy Principle for a Polyatomic Gas Subject to the Dynamic Pressure
Vol. 11 No. 1 (2016) P.1~P.22
We establish Extended Thermodynamics (ET) of rarefied polyatomic gases with six
independent fields, i.e., the mass density, the velocity, the temperature and the dynamic
pressure, without adopting the near-equilibrium approximation. The closure is accomplished
by the Maximum Entropy Principle (MEP) adopting a distribution function that
takes into account the internal degrees of freedom of a molecule. The distribution function
is not necessarily near equilibrium. The result is in perfect agreement with the phenomenological
ET theory. To my knowledge, this is the first example of molecular extended
thermodynamics with a non-linear closure. The integrability condition of the moments
requires that the dynamical pressure should be bounded from below and from above. In
this domain the system is symmetric hyperbolic. Finally we verify the K-condition for this
model and show the existence of global smooth solutions.
Extended Thermodynamics, Non-Equilibrium Fluids, Symmetric Hyperbolic systems, Maximum Entropy Principle.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35L, 76A, 76P.
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Revised : 2015-06-29