On the existence of global attractors of the approximate deconvolution models of turbulence

In this report we consider the problem of the existence of global attractors of the weak solution of the approximate deconvolution models of turbulence. The L2-global attractors are known to exist for large eddy simulation models such as Leray-alpha, Leray-deconvolution or NS-omega models. In the case of the approximate deconvolution model, as the L2 norm of the weak solution of the ADM is not controlled by the L2-norm of the initial data and the approximate deconvolution model is an approximation of the filtered NSE, we are led to the question of existence of H1-global attractors. We also prove better regularity of the weak solution of ADM.