Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing

Ryan McConnell

doi:10.3934/dcdsb.2022115

Article Contents

2023, Volume 28, Issue 2: 1133-1158. Doi: 10.3934/dcdsb.2022115

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Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing

Ryan McConnell

Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA

Received: February 2022

Revised: May 2022

Early access: June 2022

Published: February 2023

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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). $

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Mathematics Subject Classification: Primary: 35Q53, 35B41; Secondary: 35B65.

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