| Abstract: |
| We consider a stochastic version of the Allen-Cahn-Navier-Stokes system in a smooth two-dimensional domain with random initial data. The system consists of a Navier-Stokes equation coupled with a convective Allen-Cahn equation, with two independent sources of randomness given by general multiplicative-type Wiener noises. In particular, the Allen-Cahn equation is characterized by a singular potential of logarithmic type as prescribed by the classical thermodynamical derivation of the model.
We analyze the long-time behavior of the (probabilistically-strong unique) solution: we establish the existence, uniqueness and asymptotic stability of the invariant measure associated to the system.
The talk is based on a joint work with A. Di Primio and L. Scarpa. |
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