A Liouville Property with Application to Asymptotic Stability for the Camassa–Holm Equation



We prove a Liouville property for uniformly almost localized (up to translations) H1-global solutions of the Camassa–Holm equation with a momentum density that is a non-negative finite measure. More precisely, we show that such a solution has to be a peakon. As a consequence, we prove that peakons are asymptotically stable in the class of H1-functions with a momentum density that belongs to \({\mathcal{M}_+(\mathbb{R})}\). Finally, we also get an asymptotic stability result for a train of peakons.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut Denis PoissonUniversité de Tours, Université d’Orléans, CNRSToursFrance

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