Global attractor for the Navier–Stokes equations with fractional deconvolution

Abstract

We consider a large eddy simulation model for the 3D Navier–Stokes equations obtained through fractional deconvolution of generic order. The global well-posedness of such a problem is already known. We prove the existence of the global attractor for the solution operator and find estimates for its Hausdorff and fractal dimensions both in terms of the Grashoff number and in terms of the mean dissipation length, with particular attention to the dependence on the fractional and deconvolution parameters. These results can be interpreted as bounds for the number of degrees of freedom of long-time dynamics, thus providing further information on the validity of the model for the simulation of turbulent 3D flows

On the convergence rates for the three‐dimensional filtered Boussinesq equations

“…Other possible regularization schemes for the system (1.4)–(1.6) are those that use anisotropic filters (see, e.g., [3, 5, 6, 12]) or those that exploit the deconvolution operator of general order N (the current case corresponds to ) as in [1, 8, 10, 16, 20, 27].…”