Weak solutions to lubrication equations in the presence of strong slippage
Georgy Kitavtsev, Philippe Laurençot, and Barbara Niethammer
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Submission date: 02. Nov. 2010 (revised version: November 2010)
published in: Methods and applications of analysis, 18 (2011) 2, p. 183-202
DOI number (of the published article): 10.4310/MAA.2011.v18.n2.a4
Keywords and phrases: lubrication equations, global weak solutions, strong slippage
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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.