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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
66/2010

Weak solutions to lubrication equations in the presence of strong slippage

Georgy Kitavtsev, Philippe Laurençot and Barbara Niethammer

Abstract

The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hydrophobyzed substrates and take account of large slippage at the polymer-substrate interface. The convergence of these solutions as either the Reynolds number or the capillarity goes to zero, as well as their limiting behaviour as the slip length goes to zero or infinity are investigated.

Received:
02.11.10
Published:
04.11.10
Keywords:
lubrication equations, global weak solutions, strong slippage

Related publications

inJournal
2011 Repository Open Access
Georgy Kitavtsev, Philippe Laurencot and Barbara Niethammer

Weak solutions to lubrication equations in the presence of strong slippage

In: Methods and applications of analysis, 18 (2011) 2, pp. 183-202