Geodesic
On the statistical derivation of hydrodynamic equations of grad type
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 414-418 Cet article a éte moissonné depuis la source Math-Net.Ru

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Hydrodynamic equations corresponding to Grad's 13-moment approximation are derived in the linear approximation in the departure from equilibrium. These equations are derived h the conditions that the mean values with respect to Zubarev's nonequilibrium ensemble be equal to those with respect to the quasiequilibrium ensemble for the quantities that characterize the state of the system, which is simpler than the ordinary method of averaging the equations of motion. The theological relations that are obtained agree with the results of [2], and, under the assumption that the momentum correlation time is much longer than the correlation time of the coordinate functions, a relaxation equation is obtained for the density of the heat flux that agrees with the corresponding equation obtained by Grad. 
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     author = {V. A. Savchenko},
     title = {On the statistical derivation of hydrodynamic equations of grad type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {414--418},
     year = {1973},
     volume = {16},
     number = {3},
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V. A. Savchenko. On the statistical derivation of hydrodynamic equations of grad type. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 414-418. http://geodesic.mathdoc.fr/item/TMF_1973_16_3_a12/

[1] D. N. Zubarev, Neravnovesnaya statisticheskaya termodinamika, «Nauka», 1971

[2] V. A. Savchenko, T. N. Khazanovich, TMF, 14 (1973), 388 | Zbl

[3] H. Grad, Commun. Pure Appl. Math., 2 (1949), 331 ; G. Gred, Mekhanika, no. 4, 71; 1952, No 5, 61 | DOI | MR | Zbl