A LIOUVILLE PROPERTY WITH APPLICATION TO ASYMPTOTIC STABILITY FOR THE CAMASSA-HOLM EQUATION

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.
Type de document :
Pré-publication, Document de travail
To appear in ARMA. 2018
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https://hal.archives-ouvertes.fr/hal-01768549
Contributeur : Luc Molinet <>
Soumis le : mardi 17 avril 2018 - 12:04:28
Dernière modification le : jeudi 3 mai 2018 - 15:26:02

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Luc Molinet. A LIOUVILLE PROPERTY WITH APPLICATION TO ASYMPTOTIC STABILITY FOR THE CAMASSA-HOLM EQUATION. To appear in ARMA. 2018. 〈hal-01768549〉

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