The Cauchy problem to a gkCH equation with peakon solutions

Abstract

Considered in this paper is a generalized Camassa-Holm equation, which includes both the Camassa-Holm equation and the Novikov equation as two special cases. Firstly, two blow-up criteria are established for the generalized Camassa-Holm equation. Then we derive two blow-up phenomena, where a new L2k estimate plays a crucial role. In addition, we also show that peakon solutions are global weak solutions.

Keywords

• l^2k estimate
• blow-up solutions
• blow-up phenomena
• peakon solutions
• generalized camassa-holm equation