# Navier-Stokes equations in the whole space with an eddy viscosity

## TL;DR

This paper investigates the Navier-Stokes equations with an added eddy viscosity term in three dimensions, establishing existence of regular solutions and their convergence to turbulent solutions as regularization diminishes.

## Contribution

Introduces a regularized system for Navier-Stokes with eddy viscosity and proves convergence to turbulent solutions as regularization parameter approaches zero.

## Key findings

- Existence of global regular solutions for the regularized system
- Convergence of regularized solutions to turbulent solutions of the original system
- Framework for analyzing turbulence via eddy viscosity models

## Abstract

We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space in three dimensions. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove that when the regularizing parameter goes to zero, the solution of the regularized system converges to a turbulent solution of the initial system.