Stochastic diffuse interface models with conservative noise

Cahn-Hilliard type models are widely used to model phase separation phenomena occurring in multicomponent systems subject to thermodynamical stress. In 1970, a stochastic variant taking into account thermal effects driving spinodal decomposition was proposed by H. Cook. This model generalizes its deterministic counterpart and better fits available experimental data, especially in the early stages of phase separation. In this talk, I will examine the stochastic analysis of an almost-surely mass-conserving stochastic Cahn-Hilliard model, which stems from the original Cahn-Hilliard-Cook model when endowed with a conservative noise in divergence form. The mass conservation property is indeed expected in the deterministic version of the system. Our first-step investigation concerns the existence of unique probabilistically strong solutions to the equation, appealing to stochastic variational techniques. Some insights on the corresponding Allen-Cahn relaxation, for which we show conditional results, will also be given. In all models, a thermodynamical singular potential is considered. Further open questions will also be presented.