Comptes Rendus
Rigorous justification of the Reynolds equations for gas lubrication
Comptes Rendus. Mécanique, Volume 333 (2005) no. 7, pp. 534-541.

The goal of this Note is to give a rigorous justification of the compressible Reynolds model for gas lubrication, via asymptotic analysis. We start from the equations of motion of compressible viscous fluid in a thin domain and study the limit as the domain thickness tends to zero. At the limit we find the known engineering model. The key of the proof is the strong convergence for the pressure obtained by its decomposition.

Le but de cette Note est de donner une justification de modèle de Reynolds compressible via une analyse asymptotique. À partir des équations de mouvement d'un fluide visqueux compressible dans un domaine mince nous étudions la limite lorsque l'épaisseur du domaine tend vers 0. À la limite nous trouvons un modèle de Reynolds compressible. La clé de la preuve est la convergence forte de la pression obtenue par la décomposition.

Published online:
DOI: 10.1016/j.crme.2005.06.006
Keywords: Lubrication, Compressible fluid, Gas lubrication, Magnetic hard disk, Rigorous asymptotic analysis
Mot clés : Lubrification, Fluide compressible, Lubrication par gaz, Disque dur magnétique, Analyse asymptotique rigoureuse

Eduard Marušić-Paloka 1; Maja Starčević 1

1 Department of Mathematics, University of Zagreb, Bijenička 30, Zagreb, Croatia
     author = {Eduard Maru\v{s}i\'c-Paloka and Maja Star\v{c}evi\'c},
     title = {Rigorous justification of the {Reynolds} equations for gas lubrication},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {534--541},
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Eduard Marušić-Paloka; Maja Starčević. Rigorous justification of the Reynolds equations for gas lubrication. Comptes Rendus. Mécanique, Volume 333 (2005) no. 7, pp. 534-541. doi : 10.1016/j.crme.2005.06.006.

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