Inertial manifold

Summary

An inertial manifold of a dissipative evolution equation is a finite-dimensional Lipschitz manifold in the infinite-dimensional phase space. It is invariant and attracts all solutions exponentially fast. It contains the global attractor. Restricted to it, the equation becomes a system of finitely many ordinary differential equations, the inertial form, which carries the full long-time dynamics. Inertial manifolds were introduced by Foias, Sell and Temam in the 1980s. They exist for many dissipative PDEs whose linear part has large gaps in its spectrum.