Well-posedness of the Cauchy problem for a shallow water equation on the circle

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:161

Article

Himonas, AA ; Misiolek, C

关键词: Cauchy problem;    well-posedness;    Sobolev spaces;    Fourier transform;   

DOI  :  10.1006/jdeq.1999.3695

来源: Elsevier

【 摘 要 】

In this paper we consider the periodic Cauchy problem for a fifth order modification of the Camassa-Holm equation. We prove local well-posedness in appropriate Bourgain spaces for initial data in a Sobolev space H-s(T), s >1/2. We also prove global well-posedness for data in H-1(T) and of arbitrary size. The proofs are based on a priori estimates using Fourier analysis techniques, microlocalization in phase space, an interpolation argument and a fixed point theorem. (C) 2000 Academic Press.

【 授权许可】

Free