INERTIAL MANIFOLDS WITH DELAY

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