Local well-posedness and global existence for a multi-component Novikov equation

Abstract

Considered herein is a multi-component Novikov equation, which admits bi-Hamiltonian structure, infinitely many conserved quantities and peaked solutions. In this paper, we deduce two blow-up criteria for this system and global existence for some two-component case in $H^s$. Finally, we verify that the system possesses peakons and periodic peakons.

Keywords:

• Well-posedness
• blow-up
• global existence
• peakon

2010 Mathematics Subject Classifications:

• 35G25
• 35B44
• 35C07

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Zhigang Li's research is supported partially by National Natural Science Foundation of China (NSFC) [Grant Nos. 11871471, 11931017]. Yuxi Hu's research is supported by NSFC [Grant No. 11701556].