Asymptotic smoothing and the global attractor of a weakly damped KdV equation on the real line

[摘要] The existence of the global attractor of a weakly damped, forced Korteweg-de Vries equation in the phase space L-2(R) is proved. An optimal asymptotic smoothing effect of the equation is also shown, namely, that for forces in L-2(R), the global attractor in the phase space L-2(R) is actually a compact set in H-3(R). The energy equation method is used in conjunction with a suitable splitting of the solutions; the dispersive regularization properties of the equation in the context of Bourgain spaces are extensively exploited. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-10

[关键词] Korteweg-de Vries equation;weak damping;noncompact system;global attractor;asymptotic smoothing;dispersive regularization;Bourgain spaces