Moderate deviation principles for stochastic 2D hydrodynamics-type systems with multiplicative jump noise

This paper establishes a moderate deviation principle for a class of stochastic 2D hydrodynamical-type systems driven by multiplicative jump noise. The proof does not require compactness of the embedding in the associated Gelfand triple, so the result applies to both bounded and unbounded domains. The combination of finite-dimensional projections and integration by parts is used to prove the strong continuity of the skeleton solution map with respect to weakly convergent controls. This approach avoids the time discretization and intricate jump estimates used in earlier treatments of noncompact settings.