Geodesic
Kinetic Equations and the Chapman--Enskog Projection Problem
Informatics and Automation, Differential equations and dynamical systems, Tome 250 (2005), pp. 219-225

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It is well known that in the low-frequency cutoffs of the Chapman–Enskog projection of moment approximations of the Boltzmann kinetic equation, the so-called ultraviolet catastrophe occurs. For the first time, this phenomenon was pointed out by A. V. Bobylev in 1992 in the simplest mode (of one-dimensional linear deviation from global equilibrium). By an example of moment approximation of the Boltzmann–Peierls kinetic equation, we prove the existence of a Chapman–Enskog projection to the phase space of the conservative variable in the class of first-order hyperbolic pseudodifferential systems with relaxation. This result is used to explain the phenomenon of ultraviolet catastrophe. 
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     author = {E. V. Radkevich},
     title = {Kinetic {Equations} and the {Chapman--Enskog} {Projection} {Problem}},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2005_250_a10/}
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E. V. Radkevich. Kinetic Equations and the Chapman--Enskog Projection Problem. Informatics and Automation, Differential equations and dynamical systems, Tome 250 (2005), pp. 219-225. http://geodesic.mathdoc.fr/item/TRSPY_2005_250_a10/