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

作者：Li, Yongsheng^*; Yan, Wei; Yang, Xingyu

来源：Journal of Evolution Equations, 2010, 10(2): 465-486.

DOI：10.1007/s00028-010-0057-z

• Well-posedness
• Modified Camassa-Holm equation
• Fourier restriction norm method
• Bilinear estimates

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 H(s) (R) with s > -n + (5)/(4), n is an element of N(+). As a consequence of the conservation of the energy parallel to u parallel to(H1(R)), we have the global well-posedness for the initial data in H(1)(R).

• 出版日期2010-5
• 单位华南理工大学