Variétés inertielles des équations différentielles dissipatives. (Inertial manifolds for dissipative differential equations). (French) Zbl 0591.35062

Summary: This note and the next one (see the following review) are a summary of our ongoing research on finite dimensional invariant Lipschitz manifolds of dissipative PDE’s or ODE’s, which contain all the attractors and attract exponentially all solutions. In this work we need a spectral condition on the linear dissipative term of the equations under consideration, which excludes the Navier-Stokes equations but includes other important equations (see the following reviews Zbl 0591.35063 and Zbl 0591.35064).


35Q99 Partial differential equations of mathematical physics and other areas of application
58J99 Partial differential equations on manifolds; differential operators
37-XX Dynamical systems and ergodic theory