21.10.2024 15:00 Max Sauerbrey:
Solution theory for the stochastic thin film equation with spatially colored noise.MI 03.06.011 (Boltzmannstr. 3, 85748 Garching)
We present recent results on the local in time well-posedness of stochastic thin-film equations driven by Gaussian noise, which is white in time and colored in space, with strictly positive initial data. We state the local well-posedness and instantaneous regularization result in any space dimension, including corresponding blow-up criteria. Then we comment on the one-dimensional situation in which global in time well-posedness can be obtained under consideration of intermolecular van der Waals forces between the fluid and the substrate.. The talk is based on joint work with Antonio Agresti: https://arxiv.org/abs/2403.12652