**Partial Differential Equations**

Parabolic partial differential equations may have finite-dimensional attractors. The diffusive part of the equation damps higher frequencies and in some cases leads to a global attractor. The *Ginzburg–Landau*, the *Kuramoto–Sivashinsky*, and the two-dimensional, forced Navier–Stokes equations are all known to have global attractors of finite dimension.

For the three-dimensional, incompressible Navier–Stokes equation with periodic boundary conditions, if it has a global attractor, then this attractor will be of finite dimensions.

Read more about this topic: Attractor

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