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Title: Derivation of the Reynolds equation for lubrication of a rotating shaft (English)
Author: Duvnjak, Antonija
Author: Marušić-Paloka, Eduard
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 36
Issue: 4
Year: 2000
Pages: 239-253
Summary lang: English
Category: math
Summary: In this paper, using the asymptotic expansion, we prove that the Reynolds lubrication equation is an approximation of the full Navier–Stokes equations in thin gap between two coaxial cylinders in relative motion. Boundary layer correctors are computed. The error estimate in terms of domain thickness for the asymptotic expansion is given. The corrector for classical Reynolds approximation is computed. (English)
Keyword: lubrication
Keyword: Reynolds equation
Keyword: Navier-Stokes system
Keyword: lower-dimensional approximation
MSC: 35B25
MSC: 35B40
MSC: 35Q30
MSC: 76D08
idZBL: Zbl 1046.35006
idMR: MR1811168
Date available: 2008-06-06T22:26:05Z
Last updated: 2012-05-10
Stable URL:
Reference: [1] Assemien A., Bayada G., Chambat M.: Inertial Effects in the Asymptotic Behavior of a Thin Film Flow.Asymptotic.Anal., 9(1994), 177–208. Zbl 0813.35076, MR 1295293
Reference: [2] Bayada G., Chambat M.: The Transition Between the Stokes Equations and the Reynolds Equation: A Mathematical Proof.Appl. Math. Optim., 14 (1986), 73–93. Zbl 0701.76039, MR 0826853
Reference: [3] Bourgeat A., Marušić-Paloka E.: Loi d’écoulement non linéaire entre deux plaques ondulées.C.R.Acad.Sci.Paris, Série I , t.321 (1995), 1115–1120. Zbl 0841.76082, MR 1360583
Reference: [4] Bourgeat A., Marušić-Paloka E.: Nonlinear Effects for Flow in Periodically Constricted Channel Caused by High Injection Rate.Math.Models Methods Appl.Sci., Vol 8, No 3 (1998), 379–405. Zbl 0920.76082, MR 1624867
Reference: [5] Capriz G.: On the Vibrations of Shaft Rotating on Lubricated Bearings.Ann. Math. Pure. Appl., 50(1960), 223–248. MR 0115378
Reference: [6] Cimatti G.: A Rigorous Justification of the Reynolds Equation.Quart. Appl. Math., XLV (4) (1987), 627–644. Zbl 0661.76028, MR 0917014
Reference: [7] Elrod H. G.: A Derivation of the Basic Equations for Hydrodynamics Lubrication with a Fluid Having Constant Properties.Quart. Appl. Math. 27 (1960), 349–385. MR 0109552
Reference: [8] Galdi G. P.: An Introduction to the Mathematical Theory of the Navier–Stokes Equations, I, II.Springer–Verlag, Berlin, 1994. MR 2808162
Reference: [9] Iosifyan G. A., Oleinik O. A.: O povedenii na beskonečnosti rešenij elliptičeskih uravnenij vtorogo porjadka v oblastjah s nekompaktnoj granicej.Mat. Sb., 112, 4(8) (1980), 588–610. MR 0587039
Reference: [10] Hughes T. J. R., Marsden J. E.: A Short Course in Fluid Mechanics.Publish or Perish, Boston, 1976. Zbl 0329.76001, MR 0468526
Reference: [11] Marušić-Paloka E.: The Effects of Torsion and Flexion for a Fluid Flow Through a Curved appear in Appl. Math. Optim. MR 1851740
Reference: [12] Nazarov S.A.: Asymptotic solution of the Navier-Stokes problem on the flow of a thin layer of fluid.Siberian Math.J., 31 (1990) 2, 296–307. Zbl 0712.76037, MR 1065588
Reference: [13] Reynolds O.: On the Theory of Lubrication and its Application to Beauchamp Tower’s Experiment.Phil. Trans. Roy. Soc. London, A 117 (1886), 157–234.
Reference: [14] Wannier G. H.: A Contribution to the Hydrodynamics of Lubrication.Quart. Appl. Math., 8 (1950), 1–32. Zbl 0036.25804, MR 0037146


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