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. After introducing the underlying model, 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.
Per informazioni, rivolgersi a: antonio.agresti@uniroma1.it