## 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

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