Eur. Phys. J. E (2013) 36: 82
https://doi.org/10.1140/epje/i2013-13082-3

Regular Article

Intermediate asymptotics of the capillary-driven thin-film equation

Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, Paris, France

^* e-mail: thomas.salez@espci.fr

Received: 24 May 2013
Accepted: 10 June 2013
Published online: 9 August 2013

Abstract

We present an analytical and numerical study of the two-dimensional capillary-driven thin-film equation. In particular, we focus on the intermediate asymptotics of its solutions. Linearising the equation enables us to derive the associated Green’s function and therefore obtain a complete set of solutions. Moreover, we show that the rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the rescaled Green’s function. Finally, a numerical study on compact-support initial profiles enables us to conjecture the extension of our results to the nonlinear equation.