On the Rate of Convergence of the Two-dimensional Α-models of Turbulence to the Navier-stokes Equations

Rates of convergence of solutions of various two-dimensional α−regularization models, subject to periodic boundary conditions, toward solutions of the exact Navier-Stokes equations are given in the L-L time-space norm, in terms of the regularization parameter α, when α approaches zero. Furthermore, as a paradigm, error estimates for the Galerkin approximation of the exact two-dimensional Leray-α model are also presented in the L-L time-space norm. Simply by the triangle inequality, one can reach the error estimates of the solutions of Galerkin approximation of the α-regularization models toward the exact solutions of the Navier-Stokes equations in the two-dimensional periodic boundary conditions case. MSC Classification: 35A30, 35Q35, 65M12, 65M15, 76D05.