Large Eddy Simulation for Turbulent Flows with Critical Regularization

TL;DR

This paper proves the existence and uniqueness of solutions for critical regularized LES models of turbulence, demonstrating convergence to classical solutions for Navier-Stokes and Magnetohydrodynamics equations.

Contribution

It establishes the mathematical foundation for critical LES models, showing their well-posedness and convergence properties for turbulence simulations.

Findings

Existence and uniqueness of regular weak solutions for critical LES.

Convergence of LES solutions to Navier-Stokes solutions as averaging radius decreases.

Extension of results to Magnetohydrodynamics equations.

Abstract

In this paper, we establish the existence of a unique "regular" weak solution to the Large Eddy Simulation (LES) models of turbulence with critical regularization. We first consider the critical LES for the Navier-Stokes equations and we show that its solution converges to a solution of the Navier-Stokes equations as the averaging radii converge to zero. Then we extend the study to the critical LES for Magnetohydrodynamics equations.