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  "body": "\n## Summary\n\nAn inertial manifold of a dissipative evolution equation is a finite-dimensional Lipschitz manifold in the infinite-dimensional phase space.\nIt is invariant and attracts all solutions exponentially fast.\nIt contains the [[global attractor|4SH2ZB984E]].\nRestricted to it, the equation becomes a system of finitely many ordinary differential equations, the inertial form, which carries the full long-time dynamics.\nInertial manifolds were introduced by Foias, Sell and Temam in the 1980s.\nThey exist for many dissipative PDEs whose linear part has large gaps in its spectrum.\n\n## Explanations\n\n### L1 human\n\nMany physical systems, like a fluid or a chemical reaction spread over space, need infinitely many numbers to describe their state.\nYet after a short time their behaviour often looks as if only a few numbers mattered.\nAn inertial manifold makes this precise: it is a finite-dimensional surface in the space of states that all solutions approach very fast.\nOnce a solution is near it, the motion is governed by finitely many equations.\n",
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