Asymptotic stability of peakons for the Novikov equation

  title={Asymptotic stability of peakons for the Novikov equation},
  author={Jos'e Manuel Palacios},
  journal={arXiv: Analysis of PDEs},
  • 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