# Asymptotic stability of peakons for the Novikov equation

@article{Palacios2020AsymptoticSO,
title={Asymptotic stability of peakons for the Novikov equation},
author={Jos'e Manuel Palacios},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Jos'e Manuel Palacios
• Published 2020
• Mathematics
• arXiv: Analysis of PDEs
• The Novikov equation is a Camassa-Holm type equation with cubic nonlinearity. This paper aims to prove the asymptotic stability of peakons solutions under $H^1(\mathbb{R})$-perturbations satisfying that their associated momentum density defines a non-negative Radon measure. Motivated by Molinet's work, we shall first prove a Liouville property for $H^1(\mathbb{R})$ global solutions belonging to a certain class of \emph{almost localized} functions. More precisely, we show that such solutions… CONTINUE READING

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## $W^{1,\infty}$ instability of $H^1$-stable peakons in the Novikov equation

• Mathematics, Physics
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