Weak solutions to lubrication systems describing the evolution of bilayer thin films

2012/11/09 by Sebastian Jachalski, Jachalski, Sebastian, Georgy Kitavtsev +3
Mathematics · #35D30 #76A20 #76D08 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35D30 #msc:76A20 #msc:76D08

paper · pdf · doi:10.48550/arxiv.1211.2216

arxiv created 2012/11/09 · arxiv updated 2012/11/12

Abstract

The existence of global nonnegative weak solutions is proved for coupled one-dimensional lubrication systems that describe the evolution of nanoscopic bilayer thin polymer films that take account of Navier-slip or no-slip conditions at both liquid-liquid and liquid-solid interfaces. In addition, in the presence of attractive van der Waals and repulsive Born intermolecular interactions existence of positive smooth solutions is shown.

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