Global attractor for the periodic generalized korteweg-de vries equation through smoothing

arxiv（2023）

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摘要

We establish a smoothing result for the generalized KdV (gKdV) on the torus with polynomial non-linearity, damping, and forcing that matches the smoothing level for the gKdV at H-1. As a consequence, we establish the existence of a global attractor for this equation as well as its compactness in H-s(T), s is an element of(1, 2).

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关键词

KdV,Korteweg-De Vries,generalized Korteweg-De Vries,non-linear smoothing,global attractor,normal form

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