A rigorous justification of the Reynolds equation
Author:
Giovanni Cimatti
Journal:
Quart. Appl. Math. 45 (1987), 627-644
MSC:
Primary 76N10; Secondary 35Q10, 76D08
DOI:
https://doi.org/10.1090/qam/917014
MathSciNet review:
917014
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A small parameter technique is used to derive Reynolds’ lubrication equation from the Stokes equation. The error associated with the approximation is estimated in suitable norms.
G. Adler, Maggiorazione del gradiente delle funzioni armoniche mediante i loro vatori al contorno, Mem. Acc. Naz. Lincei VI, 183–201 (1961)
- Giovanni Cimatti, How the Reynolds equation is related to the Stokes equations, Appl. Math. Optim. 10 (1983), no. 3, 267–274. MR 722490, DOI https://doi.org/10.1007/BF01448389
- H. G. Elrod, A derivation of the basic equations for hydrodynamic lubrication with a fluid having constant properties, Quart. Appl. Math. 17 (1959/60), 349–359. MR 109552, DOI https://doi.org/10.1090/S0033-569X-1960-0109552-X
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190
A. Gross, Fluid film lubrication, John Wiley, 1980
- O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Mathematics and its Applications, Vol. 2, Gordon and Breach, Science Publishers, New York-London-Paris, 1969. Second English edition, revised and enlarged; Translated from the Russian by Richard A. Silverman and John Chu. MR 0254401
- Carlo Miranda, Formule di maggiorazione e teorema di esistenza per le funzioni biarmoniche de due variabili, Giorn. Mat. Battaglini (4) 2(78) (1948), 97–118 (Italian). MR 30058
O. Pincus and B. Sternlicht, Theory of hydrodynamic lubrication, McGraw-Hill, 1961
O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments including an experimental determination of the viscosity of olive oil, Phil. Trans. Roy. Soc. London 177, 157–234 (1886)
- Gregory H. Wannier, A contribution to the hydrodynamics of lubrication, Quart. Appl. Math. 8 (1950), 1–32. MR 37146, DOI https://doi.org/10.1090/S0033-569X-1950-37146-5
- Guy Bayada and Michèle Chambat, The transition between the Stokes equations and the Reynolds equation: a mathematical proof, Appl. Math. Optim. 14 (1986), no. 1, 73–93. MR 826853, DOI https://doi.org/10.1007/BF01442229
G. Adler, Maggiorazione del gradiente delle funzioni armoniche mediante i loro vatori al contorno, Mem. Acc. Naz. Lincei VI, 183–201 (1961)
G. Cimatti, How the Reynolds equation is related to the Stokes equations, Appl. Math. and Opt. 10, 267–274 (1983)
H. G. Elrod, A derivation of the basic equations for hydrodynamic lubrication with a fluid having constant properties, Quart. Appl. Math. 27, 349–359 (1960)
D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of the second order, Springer, 1983
A. Gross, Fluid film lubrication, John Wiley, 1980
O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, 1969
C. Miranda, Formule di maggiorazione e teorema di esistenza per le funzioni biarmoniche in due variabili, Giorn. Mat. Battaglini 78, 97–118 (1948)
O. Pincus and B. Sternlicht, Theory of hydrodynamic lubrication, McGraw-Hill, 1961
O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments including an experimental determination of the viscosity of olive oil, Phil. Trans. Roy. Soc. London 177, 157–234 (1886)
G. H. Wannier, A contribution to the hydrodynamics of lubrication, Quart. Appl. Math. 8, 1–32 (1950)
G. Bayada & M. Chambat, The transition between the Stokes and the Reynolds equation: A mathematical proof, Appl. Math. Optim. 14, 73–93 (1986)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
76N10,
35Q10,
76D08
Retrieve articles in all journals
with MSC:
76N10,
35Q10,
76D08
Additional Information
Article copyright:
© Copyright 1987
American Mathematical Society
