Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing

Ryan McConnell

Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing

Analysis of PDEs 2022-01-31 v2 Dynamical Systems

Authors: Ryan McConnell

Abstract

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 $H^s(\mathbb{T})$ , $s\in (1,2).$

Keywords

global attractor generalized kdv equation smoothing periodic boundary polynomial nonlinearity damping forcing

Cite

@article{arxiv.2105.13405,
  title  = {Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing},
  author = {Ryan McConnell},
  journal= {arXiv preprint arXiv:2105.13405},
  year   = {2022}
}

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29 pages

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