Weak solutions to lubrication equations in the presence of strong slippage

Details Weak solutions to lubrication equations in the presence of strong slippage Weak solutions to lubrication equations in the presence of strong slippage

2010-12-03

arxiv.org/abs/1012.0687v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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