Weak solutions to lubrication equations in the presence of strong slippage

TL;DR

This paper proves the existence of global weak solutions for one-dimensional lubrication models with large slippage, analyzing their behavior under various physical limits relevant to nanoscopic polymer films.

Contribution

It introduces a mathematical framework for weak solutions in lubrication equations considering strong slippage, including their convergence and limiting behaviors.

Findings

Existence of global weak solutions established.

Solutions converge as Reynolds number or capillarity approaches zero.

Behavior analyzed as slip length varies from zero to infinity.

Abstract

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.