Inertial manifolds with delay Original Research Article

The concept of inertial manifolds is implicitly based on the hypothesis of instantaneous adjustment of the small eddies to the large ones. In this article we remove this hypothesis and we introduce a concept of inertial manifold with delay (IMD), the delay time T allowing more flexibility for the adjustment of the small eddies to the large ones. We establish the existence of such manifolds which do not require a spectral gap condition.