Une variété approximante de l’attracteur universel des équations de Navier-Stokes, non linéaire, de dimension finie. (On a nonlinear finite dimensional approximative manifold to the universal attractor of the Navier-Stokes equation). (French) Zbl 0683.35073

Titi, Edriss S.

C. R. Acad. Sci., Paris, Sér. I 307, No. 8, 383-385 (1988).

Summary: We present an explicit nonlinear approximative manifold to the approximative manifold to the universal (global) attractor of the Navier- Stokes equations, of finite dimension m. In an illustrative example, we show that this manifold yields a smaller error than the flat linear manifold spanned by the first m eigenvectors of the Stokes operator.

MSC:

35Q30	Navier-Stokes equations
35K15	Initial value problems for second-order parabolic equations
35A35	Theoretical approximation in context of PDEs

Keywords:

approximative manifold; universal; attractor