Communications in Mathematical Sciences

Volume 12 (2014)

Number 3

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

Pages: 527 – 544



Sebastian Jachalski (Weierstrass Institute, Berlin, Germany)

Georgy Kitavtsev (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Roman Taranets (Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine)


The existence of global non-negative weak solutions is proved for coupled onedimensional 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 derWaals and repulsive Born intermolecular interactions existence of positive smooth solutions is shown.


bilayer systems, lubrication equations, weak solutions, slippage

2010 Mathematics Subject Classification

35D30, 76A20, 76D08

Published 26 November 2013