ASYMPTOTIC STABILITY FOR SOME NON POSITIVE PERTURBATIONS OF THE CAMASSA-HOLM PEAKON WITH APPLICATION TO THE ANTIPEAKON-PEAKON PROFILE - Archive ouverte HAL Access content directly
Journal Articles international mathematical research notices Year : 2020

ASYMPTOTIC STABILITY FOR SOME NON POSITIVE PERTURBATIONS OF THE CAMASSA-HOLM PEAKON WITH APPLICATION TO THE ANTIPEAKON-PEAKON PROFILE

Luc Molinet

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 ] − ∞, x 0 ] and the positive part in [x 0 , +∞[ for some x 0 ∈ 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 +∞,. This leads to an improvement of the asymptotic stability result stated in [29].
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Dates and versions

hal-01768579 , version 1 (17-04-2018)
hal-01768579 , version 2 (03-07-2018)

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Luc Molinet. ASYMPTOTIC STABILITY FOR SOME NON POSITIVE PERTURBATIONS OF THE CAMASSA-HOLM PEAKON WITH APPLICATION TO THE ANTIPEAKON-PEAKON PROFILE. international mathematical research notices, 2020, 21, pp.7908-7943. ⟨hal-01768579v2⟩
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