A note on the analytic solutions of the Camassa-Holm equation

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Abstract

In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using theAbstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analyticsolution. Moreover, if the initial data is real analytic, belongs to H s (R) with s > 3/2, u0 L1 < ∞ and u0 − u0xx does not changesign, we prove that the solution stays analytic globally in time.
Lingua originaleEnglish
pagine (da-a)659-664
Numero di pagine6
RivistaCOMPTES RENDUS MATHÉMATIQUE
Volume341
Stato di pubblicazionePublished - 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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