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Approximation of weak limits via method of averaging with applications to Navier-Stokes equations. (English) Zbl 0990.46017
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 197-204 (2002).
Summary: We prove, firstly, that the weak limit of some sequence from Orlicz function space can be approximated in the strong sense (in norm) by the subsequence of averaged functions if the radius averaging tends to zero slowly enough. Secondly, we consider the weakly converging sequence of approximate solutions to the Navier-Stokes equations and obtain strong convergence of some subsequence of solutions to averaged equations to the solution of the limiting equations.
For the entire collection see [Zbl 0972.00046].

##### MSC:
 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 35Q30 Navier-Stokes equations