Intermediate Asymptotics of the Capillary-Driven Thin Film Equation
  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. 
Michael Benzaquen, Thomas Salez, and \'Elie Rapha\"el
math.AP cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.soft physics.flu-dyn