A Note on the Strong Convergence towards Attractors of Damped Forced KdV Equations

This note is a continuation of a previous article which appeared in this journal (1988, 74, 369-390). In the previous work we showed that a weak dissipation is suffiient to impose a finite dimensional behavior for Korteweg de Vries equations with (space) periodic boundary conditions. More precisely, it was shown that all the trajectories are captured. by a finite dimensional attractor. However, we were only able to show that the convergence of the trajectories holds good in the sense of weak topology. The goal of this note is to show that in fact this convergence holds true in the sense of strong topology.