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

TL;DR

This paper proves the existence of weak solutions for coupled lubrication systems modeling bilayer thin film evolution, considering slip conditions and intermolecular forces, advancing understanding of nanoscopic polymer film dynamics.

Contribution

It establishes the existence of global weak solutions for coupled lubrication equations with slip conditions and intermolecular interactions, a novel result in this context.

Findings

Existence of global nonnegative weak solutions for the system.

Existence of positive smooth solutions under intermolecular forces.

Analysis includes Navier-slip and no-slip boundary conditions.

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.