Strong existence and uniqueness of the stationary distribution for a   stochastic inviscid dyadic model
  We consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution. 
Luisa Andreis, David Barbato, Francesca Collet, Marco Formentin, Luigi   Provenzano
math.PR math.AP