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A justification for the thin film approximation of Stokes flow with surface tension. (English) Zbl 1387.35632

Summary: In the free boundary problem of Stokes flow driven by surface tension, we pass to the limit of small layer thickness. It is rigorously shown that in this limit the evolution is given by the well-known thin film equation. The main techniques are appropriate scaling and uniform energy estimates in Sobolev spaces of sufficiently high order, based on parabolicity.

MSC:

35R35 Free boundary problems for PDEs
76D07 Stokes and related (Oseen, etc.) flows
35K35 Initial-boundary value problems for higher-order parabolic equations
35Q30 Navier-Stokes equations
76D08 Lubrication theory
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