Persistence of invariant manifolds for nonlinear PDEs

Journal article

We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by these flows persist under $C^1$ perturbation. In particular, we extend well known finite-dimensional results to the setting of an infinite-dimensional Hilbert manifold with a semi-group that leaves a submanifold invariant. We then study the persistence of global unstable manifolds of hyperbolic fixed-points, and as an application consider the two-dimensional Navier-Stokes equation under a fully discrete approximation. Finally, we apply our theory to the persistence of inertial manifolds for those PDEs which possess them. te

Authors: Jones, D; Shkoller, S

• Publication date: 1998-07-17
• Keywords: math.AP; 35K50, 58B99, 76D05; math.DS; math.NA