Coarsening rates for the dynamics of slipping droplets

In this talk the dynamics of coarsening liquid nanoscopic droplets will be described in the framework of the lubrication approximation for different slip regimes considered at the solid substrate. We start with the introduction of underlying lubrication equations and shortly summarize existence results for them. Next, a sharp interface model for the evolution of droplets is derived in two and three dimensional cases. By that one arrives at the closed set of reduced ODE models, analytical and numerical investigation of which allows for derivation of the coarsening rates dependence on the slip-length. Finally, we discuss a possibility for the rigorous justification of the observed coarsening rates.