On a critical Leray-αα model of turbulence

This paper aims to study a family of Leray-αα models with periodic boundary conditions. These models are good approximations for the Navier–Stokes equations. We focus our attention on the critical value of regularization “θθ” that guarantees the global well-posedness for these models. We conjecture that θ=14 is the critical value to obtain such results. When alpha goes to zero, we prove that the Leray-αα solution, with critical regularization, gives rise to a suitable solution to the Navier–Stokes equations. We also introduce an interpolating deconvolution operator that depends on “θθ”. Then we extend our results of existence, uniqueness and convergence to a family of regularized magnetohydrodynamics equations.