Large Deviations Principle for the Inviscid Limit of Fluid Dynamic Systems in 2D Bounded Domains
- Authors: Federico Butori, Eliseo Luongo
- Preprint year: 2023
- First public date: 2023-05-18
- arXiv: 2305.11148
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: Electronic Journal of Probability 29, 1–42 (2024)
- DOI: 10.1214/24-EJP1238
Abstract
Using a weak convergence approach, we establish a Large Deviation Principle (LDP) for the solutions of fluid dynamic systems in two-dimensional bounded domains subjected to no-slip boundary conditions and perturbed by additive noise. Our analysis considers the convergence of both viscosity and noise intensity to zero. Specifically, we focus on three important scenarios: Navier-Stokes equations in a Kato-type regime, Navier-Stokes equations for fluids with circularly symmetric flows and Second-Grade Fluid equations. In all three cases, we demonstrate the validity of the LDP, taking into account the critical topology $C([0,T];L^2).$