The paper “Inertial manifolds for the 3D modified-Leray-α model with periodic boundary conditions“, authored by Anna Kostianko, has been accepted for publication in the Journal of Dynamics and Differential Equations.  It is published gold open access and a link to the online version is here.  The paper proves the existence of an inertial manifold for the modified Leray-α model with periodic boundary conditions in three-dimensional space using the so-called spatial averaging principle. In addition, an adaptation of the Perron method for constructing inertial manifolds in the particular case of zero spatial averaging is suggested.