Speaker
Description
We investigate the long time behavior of a stochastic Allen-Cahn-Navier-Stokes system modeling the dynamics of binary mixtures of immiscible fluids. The model features the thermodynamically relevant Flory-Huggins logarithmic potential and incorporates two stochastic forcing terms: one driving the velocity field in the Navier-Stokes equation and the other acting on the phase variable in the Allen-Cahn equation. First, we establish the existence of ergodic invariant measures. Furthermore, we prove that the stochastic flow admits a unique, asymptotically stable invariant measure, provided that the noise driving the Navier-Stokes equation is non-degenerate along sufficiently many low modes and the Allen-Cahn equation exhibits strong dissipativity. The talk is based on a joint work with A. Di Primio and L. Scarpa.