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

TL;DR

This paper investigates a multi-component Novikov equation, establishing conditions for blow-up and global existence, and confirming the presence of peakon solutions, contributing to the understanding of its mathematical properties.

Contribution

It introduces new blow-up criteria, proves global existence in certain cases, and confirms peakon solutions for the multi-component Novikov equation.

Findings

Derived two blow-up criteria for the system.

Proved global existence for specific two-component cases.

Verified the existence of peakons and periodic peakons.

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.