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Mathematics > Analysis of PDEs

arXiv:1804.06230 (math)
[Submitted on 17 Apr 2018 (v1), last revised 3 Jul 2018 (this version, v2)]

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

Authors:Luc Molinet (IDP)
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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].
Comments: In this second version, we improve the result in the appendix by proving that for a solution with 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 for such solutions. arXiv admin note: text overlap with arXiv:1804.06225
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.06230 [math.AP]
  (or arXiv:1804.06230v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.06230

Submission history

From: Luc Molinet [view email] [via CCSD proxy]
[v1] Tue, 17 Apr 2018 13:31:27 UTC (25 KB)
[v2] Tue, 3 Jul 2018 09:37:38 UTC (27 KB)
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