A note on the Cauchy problem of the Novikov equation

In this article, we mainly study the Cauchy problem of the Novikov equation. We first establish local well-posedness of the equation in Besov space . Then we derive a lower bound for the maximal existence time and lower semicontinuity of the existence time. Finally, we prove that the equation is ill-posed in by peakon solutions which exist globally in time to the equation.