AIMS Mathematics (May 2022)
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