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Mathematics > Analysis of PDEs

arXiv:1804.06225 (math)
[Submitted on 17 Apr 2018]

Title:A liouville property with application to asymptotic stability for the camassa-holm equation

Authors:Luc Molinet (IDP)
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Abstract:We prove a Liouville property for uniformly almost localized (up to translations) H 1-global solutions of the Camassa-Holm equation with a momentum density that is a non negative finite measure. More precisely, we show that such solution has to be a peakon. As a consequence, we prove that peakons are asymptotically stable in the class of H 1-functions with a momentum density that belongs to M + (R). Finally, we also get an asymptotic stability result for train of peakons.
Comments: To appear in ARMA
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.06225 [math.AP]
  (or arXiv:1804.06225v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.06225
Related DOI: https://doi.org/10.1007/s00205-018-1243-3

Submission history

From: Luc Molinet [view email] [via CCSD proxy]
[v1] Tue, 17 Apr 2018 13:27:45 UTC (35 KB)
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