Scaling Limit and Large Deviation for 3D Globally Modified Stochastic Navier-Stokes Equations with Transport Noise

TL;DR

This paper investigates the behavior of 3D globally modified stochastic Navier-Stokes equations with transport noise, establishing existence, uniqueness, convergence to deterministic solutions, and a large deviation principle.

Contribution

It introduces a rigorous analysis of the stochastic hyperviscous Navier-Stokes equations, including existence, uniqueness, scaling limit convergence, and large deviation principles.

Findings

Existence and pathwise uniqueness of weak solutions.

Convergence of stochastic solutions to deterministic ones in a scaling limit.

Establishment of a large deviation principle for the stochastic system.

Abstract

We consider the globally modified stochastic (hyperviscous) Navier-Stokes equations with transport noise on 3D torus. We first establish the existence and pathwise uniqueness of the weak solutions, and then show their convergence to the solutions of the deterministic 3D globally modified (hyperviscous) Navier-Stokes equations in an appropriate scaling limit. Furthermore, we prove a large deviation principle for the stochastic globally modified hyperviscous system.