A thin film is a fluid with thickness typically ranging from a nanometer to several micrometers. During the last decades there has been an intense study regarding the mathematical modeling and analysis of thin film equations. Most of these investigations consider the case of Newtonian thin films. While many common liquids, such as water, may reasonably be considered Newtonian, there is a multitude of fluids appearing in applications, which are in fact non-Newtonian.
In this talk, I will discuss the modeling and some analysis of non-Newtonian thin-film equations. Applying so-called lubrication approximation, the evoluion equation for the thin film height is degenerate, parabolic and of fourth order with generally merely Hölder-continuous dependence on the coefficients. Problems regarding existence and uniqueness of solutions as well as asympotitic long time behavior will be adressed.