an:04149741
Zbl 0701.76039
Bayada, Guy; Chambat, Mich??le
The transition between the Stokes equations and the Reynolds equation: A mathematical proof
EN
Appl. Math. Optimization 14, 73-93 (1986).
00151718
1986
j
76D07 35Q30
Reynolds equation; thin layer of lubricant film; Stokes equations
Summary: The Reynolds equation is used to calculate the pressure distribution in a thin layer of lubricant film between two surfaces. Using the asymptotic expansion in the Stokes equations, we show the existence of singular perturbation phenomena whenever the two surfaces are in relative motion. We prove that the Reynolds equation is an approximation of the Stokes equations and that the kind of convergence is strongly related with the boundary conditions on the velocity field.