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.

published proceedings

  • JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

altmetric score

  • 3

author list (cited authors)

  • TITI, E. S.

citation count

  • 148

complete list of authors

  • TITI, ES

publication date

  • July 1990