Large Eddy Simulation for turbulent flows with critical regularization

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 magnetohydrodynamic equations.