The Cauchy problem to a gkCH equation with peakon solutions

Abstract

<abstract><p>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 $ L^{2k} $ estimate plays a crucial role. In addition, we also show that peakon solutions are global weak solutions.</p></abstract>