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Inertial effects in the asymptotic behavior of a thin film flow. (English) Zbl 0813.35076

Summary: We study the dependence with respect to the domain of the constants appearing in some Sobolev embeddings. It shows that the inertial effects are negligible at the first order for the asymptotic behavior of a thin film flow. The influence of the inertial effects is obtained at the second order in the asymptotic expansions of the pressure and velocity, with full convergence argument for chosen boundary conditions.

MSC:

35Q30 Navier-Stokes equations
76D08 Lubrication theory
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