| Abstract: |
| In this talk we present the study of the long-time behaviour of a stochastic Allen-Cahn-Navier-Stokes system. The model features two stochastic forcings, one on the velocity in the Navier-Stokes equation and one on the phase variable in the Allen-Cahn equation, and includes the thermodynamically relevant Flory-Huggins logarithmic potential. We first show existence of ergodic invariant measures. Secondly, we prove that if the noise acting in the Navier-Stokes equation is nondegenerate along a sufficiently large number of low modes, and the Allen-Cahn equation is highly dissipative, then the stochastic flow admits a unique invariant measure which is asymptotically stable with respect to a suitable Wasserstein metric. The talk is based on a joint work with A. Di Primio and L. Scarpa. |
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