Moderate deviation principles for stochastic 2D hydrodynamics type systems with multiplicative L\'evy noise

TL;DR

This paper proves a moderate deviation principle for a class of stochastic 2D hydrodynamics equations driven by Le9vy noise, broadening understanding of their probabilistic behavior without relying on compact embedding assumptions.

Contribution

It establishes a moderate deviation principle for stochastic 2D hydrodynamics models with Le9vy noise, removing the need for compact embedding assumptions.

Findings

Moderate deviation principle proven for stochastic 2D hydrodynamics systems.

Applicable to various models including Navier-Stokes and MHD equations.

Uses weak convergence method to achieve results.

Abstract

In this paper, we establish a moderate deviation principle for an abstract nonlinear equation forced by random noise of L\'evy type. This type of equation covers many hydrodynamical models, including stochastic 2D Navier-Stokes equations, stochastic 2D MHD equations, the stochastic 2D magnetic B\'ernard problem, and also several stochastic shell models of turbulence. This paper gets rid of the compact embedding assumption on the associated Gelfand triple. The weak convergence method plays an important role.