Special Session 4: Control and Optimization

Martingale solutions to the stochastic thin film equation

Manuel V Gnann
TU Delft
Netherlands
Co-Author(s):    Konstantinos Dareiotis, Benjamin Gess, Guenther Gruen
Abstract:
We prove existence of nonnegative martingale solutions to the stochastic thin-film equation with Stratonovich noise. In the first part of the talk, I will give a proof of existence for quadratic mobilities and linear gradient noise based on a Trotter-Kato scheme, essentially only building up on dissipation of the surface energy. In the second part, I will then discuss how to treat general mobilities and nonlinear gradient noise, which additionally requires the use of entropy functionals.