Singularities in Finite Time of a Two‐Component Peakon System With Cubic Nonlinearity

ABSTRACT Blow‐up of the two‐component peakon system with cubic nonlinearity is significant and fascinating for physicists and mathematicians. In the paper, by exploiting the fine structure of the system and the conservation law , we obtain nonlinear estimates on the ‐norm of the strong solution during its lifespan, both with and without dependence on the ‐norm assumption. Thus, two new blow‐up results are derived.