Moderate deviations for stochastic models of two-dimensional second grade fluids driven by L'evy noise

TL;DR

This paper proves a moderate deviation principle for 2D second grade fluid models influenced by Lévy noise, highlighting differences from Gaussian-driven models due to jumps, using a weak convergence approach.

Contribution

It introduces a moderate deviation principle for stochastic second grade fluids with Lévy noise, addressing the impact of jumps and extending previous Gaussian-based results.

Findings

Established a moderate deviation principle for Lévy-driven fluids

Demonstrated the significance of jumps in stochastic fluid models

Extended the weak convergence approach to Lévy noise context

Abstract

In this paper, we establish a moderate deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. We will adopt the weak convergence approach. Because of the appearance of jumps, this result is significantly different from that in Gaussian case.