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

Luc Molinet (1)

1 IDP - Institut Denis Poisson

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.

Mots clés: Camassa-Holm equation; asymptotic stability; peakon

Domaines: Equations aux dérivées partielles [math.AP]

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⟩