Derivation of the Reynolds equation for lubrication of a rotating shaft

Antonija Duvnjak; Eduard Marušić-Paloka

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 4, page 239-253
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Duvnjak, Antonija, and Marušić-Paloka, Eduard. "Derivation of the Reynolds equation for lubrication of a rotating shaft." Archivum Mathematicum 036.4 (2000): 239-253. <http://eudml.org/doc/248566>.

@article{Duvnjak2000,
abstract = {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.},
author = {Duvnjak, Antonija, Marušić-Paloka, Eduard},
journal = {Archivum Mathematicum},
keywords = {lubrication; Reynolds equation; Navier-Stokes system; lower-dimensional approximation; lubrication; Reynolds equation; Navier-Stokes system; dimensional reduction},
language = {eng},
number = {4},
pages = {239-253},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Derivation of the Reynolds equation for lubrication of a rotating shaft},
url = {http://eudml.org/doc/248566},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Duvnjak, Antonija
AU - Marušić-Paloka, Eduard
TI - Derivation of the Reynolds equation for lubrication of a rotating shaft
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 4
SP - 239
EP - 253
AB - 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.
LA - eng
KW - lubrication; Reynolds equation; Navier-Stokes system; lower-dimensional approximation; lubrication; Reynolds equation; Navier-Stokes system; dimensional reduction
UR - http://eudml.org/doc/248566
ER -

References

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  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. (1980) MR0587039
  10. Hughes T. J. R., Marsden J. E., A Short Course in Fluid Mechanics, Publish or Perish, Boston, 1976. (1976) Zbl0329.76001MR0468526
  11. Marušić-Paloka E., The Effects of Torsion and Flexion for a Fluid Flow Through a Curved Pipe, to appear in Appl. Math. Optim. MR1851740
  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. (1990) Zbl0712.76037MR1065588
  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. 
  14. Wannier G. H., A Contribution to the Hydrodynamics of Lubrication, Quart. Appl. Math., 8 (1950), 1–32. (1950) Zbl0036.25804MR0037146

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