On the regularity of the global attractor of a weakly damped, forced Korteweg-de Vries equation

Abstract

The existence of the global attractor for a weakly damped, forced Korteweg-de Vries equation is derived in higher-order Sobolev spaces. The main result is the regularity of the global attractor, which is proved to be as regular as the forcing term. This result is attained through a nonobvious decomposition of the solutions used to overcome the lack of a suitable regularization of the linear part of the equation with respect to either the initial condition or the nonhomogeneous term.