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Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface. (English) Zbl 0822.76078

Summary: The hard disk data storage surfaces of magnetic storage devices are artificially roughened, and this phenomenon induces an equation with rapidly oscillating coefficients. We give homogenization results for both continuum and slip flow problems. Proofs are based on a double-scale convergence, and a new homogenized problem is given for the slip flow problem. The existence and uniqueness of the limit solutions are given, and some numerical results are presented.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
78A55 Technical applications of optics and electromagnetic theory
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References:

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