Weak solutions to lubrication systems describing the evolution of bilayer thin films
- Jachalski, Sebastian
- Kitavtsev, Georgy
- Taranets, Roman
2010 Mathematics Subject Classification
- 35D30 76A20 76D08
- bilayer systems, lubrication equations, weak solutions, slippage
The existence of global nonnegative weak solutions is proved for coupled one-dimen- sional 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.
- Comm. Math. Sci., 12 (2014) pp. 527--544.