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arXiv · 1211.7301

Intermediate Asymptotics of the Capillary-Driven Thin Film Equation

Michael Benzaquen·Thomas Salez·Élie Raphaël
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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.

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Michael Benzaquen, Thomas Salez, Élie Raphaël. 2012-11-30. Intermediate Asymptotics of the Capillary-Driven Thin Film Equation. https://arxiv.org/abs/1211.7301

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