Gevrey regularity and analyticity for Camassa-Holm type systems

• Wei Luo ^[1] ; Zhaoyang Yin ^[2]
  1. [1] Sun Yat-sen University

     Sun Yat-sen University

     China

     
  2. [2] Macau University of Science and Technology, China
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 3, 2018, págs. 1061-1079
• Idioma: inglés
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• Resumen

  • In this paper we mainly investigate the Cauchy problem of CamassaHolm type systems. By constructing a new auxiliary function, we present a generalized Ovsyannikov theorem. By using this theorem and the basic properties of Sobolev-Gevrey spaces, we prove the Gevrey regularity and analyticity of these systems. Moreover, we obtain a lower bound of the lifespan and the continuity of the data-to-solution map