A LIOUVILLE PROPERTY WITH APPLICATION TO ASYMPTOTIC STABILITY FOR THE CAMASSA-HOLM EQUATION - Archive ouverte HAL Access content directly
Journal Articles Archive for Rational Mechanics and Analysis Year : 2018

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

Luc Molinet

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.
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hal-01768549 , version 1 (17-04-2018)

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Luc Molinet. A LIOUVILLE PROPERTY WITH APPLICATION TO ASYMPTOTIC STABILITY FOR THE CAMASSA-HOLM EQUATION. Archive for Rational Mechanics and Analysis, 2018, 230 (1), pp.185-230. ⟨10.1007/s00205-018-1243-3⟩. ⟨hal-01768549⟩
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