On the existence of an inertial manifold for a deconvolution model of the 2D mean Boussinesq equations

TL;DR

This paper proves the existence of an inertial manifold for a deconvolution model of the 2D mean Boussinesq equations, demonstrating a finite-dimensional structure that attracts solutions exponentially.

Contribution

It establishes the existence of an inertial manifold for the approximate deconvolution model of the 2D mean Boussinesq equations using Van Cittern operators.

Findings

Existence of an inertial manifold for the model.

Finite-dimensional, exponentially attracting manifold proven.

Application of Van Cittern approximate deconvolution operators.

Abstract

We show the existence of an inertial manifold (i.e. a globally invariant, exponentially attracting, finite-dimensional manifold) for the approximate deconvolution model of the 2D mean Boussinesq equations. This model is obtained by means of the Van Cittern approximate deconvolution operators, which is applied to the 2D filtered Boussinesq equations.