Geodesic
Kinetic equation method for problems of viscous gas dynamics with rapidly oscillating density distributions
Informatics and Automation, Modern problems of mechanics, Tome 281 (2013), pp. 68-83 
P. I. Plotnikov; S. A. Sazhenkov. Kinetic equation method for problems of viscous gas dynamics with rapidly oscillating density distributions. Informatics and Automation, Modern problems of mechanics, Tome 281 (2013), pp. 68-83. http://geodesic.mathdoc.fr/item/TRSPY_2013_281_a6/
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     author = {P. I. Plotnikov and S. A. Sazhenkov},
     title = {Kinetic equation method for problems of viscous gas dynamics with rapidly oscillating density distributions},
     journal = {Informatics and Automation},
     pages = {68--83},
     year = {2013},
     volume = {281},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_281_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Equations describing the dynamics of a viscous gas are considered in a bounded space–time domain. It is assumed that the boundary values of density distributions oscillate rapidly. Limit regimes that arise when the oscillation frequencies tend to infinity are studied. As a result, a limit (averaged) model is constructed that contains full information on the limit oscillation regimes and includes an additional kinetic equation that has the form of the Boltzmann equation in the kinetic theory of gases.

[1] Feireisl E., Dynamics of viscous compressible fluids, Oxford Univ. Press, Oxford, 2004 | MR | Zbl

[2] Feireisl E., Novotný A., Singular limits in thermodynamics of viscous fluids, Birkhäuser, Basel, 2009 | MR | Zbl

[3] Lions P.-L., Mathematical topics in fluid mechanics. V. 2: Compressible models, Oxford Univ. Press, New York, 1998 | MR

[4] Novotný A., Straškraba I., Introduction to the mathematical theory of compressible flow, Oxford Lect. Ser. Math. Appl., 27, Oxford Univ. Press, Oxford, 2004 | MR | Zbl

[5] Plotnikov P.I., Sokolowski J., “Inhomogeneous boundary value problem for nonstationary compressible Navier–Stokes equations”, J. Math. Sci., 170:1 (2010), 34–130 | DOI | MR

[6] Girinon V., “Navier–Stokes equations with nonhomogeneous boundary conditions in a convex bi-dimensional domain”, Ann. Inst. Henri Poincaré. Anal. non lineaire, 26:5 (2009), 2025–2053 | DOI | MR | Zbl

[7] Bakhvalov N.S., Eglit M.E., “Protsessy v periodicheskikh sredakh, ne opisyvaemye v terminakh srednikh kharakteristik”, DAN SSSR, 268:4 (1983), 836–840 | MR | Zbl

[8] Amosov A.A., Zlotnik A.A., “O kvaziosrednennykh uravneniyakh odnomernogo dvizheniya vyazkoi barotropnoi sredy s bystroostsilliruyuschimi dannymi”, ZhVMiMF, 36:2 (1996), 87–110 | MR | Zbl

[9] Málek J., Nečas J., Rokyta M., Růžička M., Weak and measure-valued solutions to evolutionary PDEs, Chapman Hall, London, 1996 | MR | Zbl

[10] Tartar L., “Compensated compactness and applications to partial differential equations”, Nonlinear analysis and mechanics: Heriot-Watt Symp., Edinburgh, 1979, V. 4, Res. Notes Math., 39, Pitman, Boston, 1979, 136–212 | MR

[11] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, T. 1, Mir, M., 1984

[12] Riss F., Sëkefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR