Inertial manifold

In mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth, invariant manifolds that contain the global attractor and attract all solutions exponentially quickly. Since an inertial manifold is finite-dimensional even if the original system is infinite-dimensional, and because most of the dynamics for the system takes place on the inertial manifold, studying the dynamics on an inertial manifold produces a considerable simplification in the study of the dynamics of the original system.

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