On the Uniqueness of Invariant Measures for the Stochastic Infinite Darcy-prandtl Number Model
نویسندگان
چکیده
The infinite Darcy-Prandtl number model is an effective reduced model for describing convection in a fluid-saturated porous medium. It is well known that the deterministic model does not possess a unique invariant measure. In this work we study the dynamics of the infinite Darcy-Prandtl number model, under an additive stochastic forcing of its low modes. This is the so-called stochastic infinite Darcy-Prandtl number model. We prove that the stochastically forced system does indeed possess a unique invariant measure.
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