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arXiv · 2305.11148

Large Deviations Principle for the Inviscid Limit of Fluid Dynamic Systems in 2D Bounded Domains

Federico Butori·Eliseo Luongo
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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 $C([0,T];L^2).$

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Federico Butori, Eliseo Luongo. 2023-05-18. Large Deviations Principle for the Inviscid Limit of Fluid Dynamic Systems in 2D Bounded Domains. https://arxiv.org/abs/2305.11148

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