Intermediate Asymptotics of the Capillary-Driven Thin Film Equation
Analysis of PDEs
2014-11-11 v3 Mesoscale and Nanoscale Physics
Materials Science
Soft Condensed Matter
Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.1211.7301,
title = {Intermediate Asymptotics of the Capillary-Driven Thin Film Equation},
author = {Michael Benzaquen and Thomas Salez and Élie Raphaël},
journal= {arXiv preprint arXiv:1211.7301},
year = {2014}
}