Periodic and Almost Periodic Random Inertial Manifolds for Non-Autonomous Stochastic Equations

TL;DR

This paper establishes the existence of random inertial manifolds for non-autonomous stochastic equations, demonstrating their periodicity and almost periodicity under specific deterministic forcing conditions.

Contribution

It introduces a Lyapunov-Perron method-based proof for inertial manifolds that incorporate both deterministic and stochastic influences, including their periodic properties.

Findings

Existence of random inertial manifolds for non-autonomous stochastic equations.

Inertial manifolds contain tempered pullback random attractors.

Pathwise periodicity and almost periodicity of manifolds under periodic and almost periodic forcing.

Abstract

By the Lyapunov-Perron method,we prove the existence of random inertial manifolds for a class of equations driven simultaneously by non-autonomous deterministic and stochastic forcing. These invariant manifolds contain tempered pullback random attractors if such attractors exist. We also prove pathwise periodicity and almost periodicity of inertial manifolds when non-autonomous deterministic forcing is periodic and almost periodic in time, respectively.