WIAS Preprint No. 1746, (2012)

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.

Appeared in

  • Comm. Math. Sci., 12 (2014) pp. 527--544.

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