Asymptotic stability for some non positive perturbations of the Camassa-Holm peakon with application to the antipeakon-peakon profile

Luc Molinet

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arXiv · 1804.06230

Asymptotic stability for some non positive perturbations of the Camassa-Holm peakon with application to the antipeakon-peakon profile

Luc Molinet

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Abstract

We continue our investigation on the asymptotic stability of the peakon. In a first step we extend our asymptotic stability result [29] in the class of functions whose negative part of the momentum density is supported in ] -- $\infty$, x 0 ] and the positive part in [x 0 , +$\infty$[ for some x 0 $\in$ R. In a second step this enables us to prove the asymptotic stability of well-ordered train of antipeakons-peakons and, in particular, of the antipeakon-peakon profile. Finally, in the appendix we prove that in the case of a non negative momentum density the energy at the left of any given point decays to zero as time goes to +$\infty$,. This leads to an improvement of the asymptotic stability result stated in [29].

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Luc Molinet. 2018-04-17. Asymptotic stability for some non positive perturbations of the Camassa-Holm peakon with application to the antipeakon-peakon profile. https://arxiv.org/abs/1804.06230

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