On approximate Inertial Manifolds to the Navier-Stokes equations
1990; Elsevier BV; Volume: 149; Issue: 2 Linguagem: Inglês
10.1016/0022-247x(90)90061-j
ISSN1096-0813
Autores Tópico(s)Numerical methods for differential equations
ResumoRecently, 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.
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