The three dimensional non-local Kelvin-Voigt fluids: Well posedness and deterministic homogenization

In this work we address the well posedness as well as the deterministic homogenization of the initial-boundary value problem for the three dimensional Navier-Stokes-Voigt equations also known as Oskolkov equations arising from Oldroyd models for non-Newtonian fluid flows. We combine some compactness arguments with the sigma-convergence method to prove that the sequence of solutions of the original problem converges in suitable topologies to the solution of an effective problem which is also an Oldroyd type model. We also prove a corrector-type result.