### Abstract

The main topic of this poster is mathematical modeling, analysis and numerical simulation of dewetting dynamics and equilibrium patterns of a thin liquid-liquid system.

We derive systems of coupled thin-film models for two immiscible liquid polymer layers on a solid substrate that account for interfacial slip and intermolecular forces. Then, we focus on the following subjects.

Investigation of stability of the two-layer system and its significant dependence on the order of magnitude of slip. The study of stationary solutions for flows of thin liquid bilayers in an energetic formulation. (We exploit the gradient flow structure of these thin-film models.) Proving the existence of global non-negative weak solutions for some of these models. Experimentally and theoretically investigation of morphological paths towards equilibrium droplets during the late stages of the dewetting process of a liquid film from a liquid substrate.