  The aim of this article is to show the global existence of both martingale
and pathwise solutions of stochastic equations with a monotone operator, of the
Ladyzenskaya-Smagorinsky type, driven by a general Levy noise. The classical
approach based on using directly the Galerkin approximation is not valid.
Instead, our approach is based on using appropriate approximations for the
monotone operator, Galerkin approximations and on the theory of martingale
solutions.
