Journal of Evolution Equations

, Volume 10, Issue 2, pp 465–486

Well-posedness of a higher order modified Camassa–Holm equation in spaces of low regularity

Article

DOI: 10.1007/s00028-010-0057-z

Cite this article as:
Li, Y., Yan, W. & Yang, X. J. Evol. Equ. (2010) 10: 465. doi:10.1007/s00028-010-0057-z

Abstract

In this paper we consider the Cauchy problem for a higher order modified Camassa–Holm equation. By using the Fourier restriction norm method introduced by Bourgain, we establish the local well-posedness for the initial data in the Hs(R) with \({s > -n+\frac{5}{4},\,n\in {\bf N}^{+}.}\) As a consequence of the conservation of the energy \({{||u||_{H^{1}(R)},}}\) we have the global well-posedness for the initial data in H1(R).

Mathematics Subject Classification (2000)

35Q53

Keywords

Well-posednessModified Camassa–Holm equationFourier restriction norm methodBilinear estimates

Copyright information

© Birkhäuser/Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsSouth China University of TechnologyGuangzhouPeople’s Republic of China