On approximate Inertial Manifolds to the Navier-Stokes equations Academic Article uri icon

abstract

  • Recently, the theory of Inertial Manifolds has shown that the long time behavior (the dynamics) of certain dissipative partial differential equations can be fully discribed by that of a finite ordinary differential system. Although we are still unable to prove existence of Inertial Manifolds to the Navier-Stokes equations, we present here a nonlinear finite dimensional analytic manifold that approximates closely the global attractor in the two-dimensional case, and certain bounded invariant sets in the three-dimensional case. This approximate manifold and others allow us to introduce modified Galerkin approximations. © 1990.

altmetric score

  • 3

author list (cited authors)

  • Titi, E. S.

citation count

  • 132

publication date

  • July 1990