Inertial manifolds for the 3D modified-Leray-$\alpha$ model with periodic boundary conditions

TL;DR

This paper proves the existence of inertial manifolds for the 3D modified-Leray-$\alpha$ model with periodic boundary conditions using the spatial averaging principle and introduces an adapted Perron method for special cases.

Contribution

It establishes the existence of inertial manifolds for a specific 3D fluid model and proposes a novel adaptation of the Perron method for zero spatial averaging cases.

Findings

Existence of inertial manifolds proved for the model.

Application of spatial averaging principle in the proof.

Introduction of an adapted Perron method for special cases.

Abstract

The existence of an inertial manifold for the modified Leray-$\alpha$ model with periodic boundary conditions in three-dimensional space is proved by using the so-called spatial averaging principle. Moreover, an adaptation of the Perron method for constructing inertial manifolds in the particular case of zero spatial averaging is suggested.