In this note we prove the well-posedness for stochastic $2D$ Navier-Stokes equation driven by general Lévy processes (in particular, $\alpha$-stable processes), and obtain the existence of invariant measures.
"Invariant measures of stochastic $2D$ Navier-Stokes equation driven by $\alpha$-stable processes." Electron. Commun. Probab. 16 678 - 688, 2011. https://doi.org/10.1214/ECP.v16-1664