2D stochastic Navier–Stokes equations driven by jump noise

In the paper, we are studying the existence and uniqueness of the solution of an abstract nonlinear equation driven by a multiplicative noise of Lévy type. Our result is formulated in an abstract setting. This type of equation covers the stochastic 2D Navier–Stokes Equations, the 2D stochastic Magneto-Hydrodynamic Equations, the 2D stochastic Boussinesq Model for the Bénard Convection, the 2D stochastic Magnetic Bérnard Problem, the 3D stochastic Leray αα-Model for the Navier–Stokes Equations and several stochastic Shell Models of turbulence.