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.
Citation
I. Moise. R. Rosa. "On the regularity of the global attractor of a weakly damped, forced Korteweg-de Vries equation." Adv. Differential Equations 2 (2) 257 - 296, 1997. https://doi.org/10.57262/ade/1366809216
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