The Cauchy problem for a unified family of integrable U(1)-invariant peakon equations from the NLS hierarchy is studied. As main results, local well-posedness is proved in Besov spaces, and blow-up is established through use of an L 1 conservation law.
Anco, Stephen C., Huijun He, and Zhijun Qiao. 2020. “Local Well-Posedness and Blow-up for a Family of $U(1)$-Invariant Peakon Equations.” ArXiv:2008.04792 [Math-Ph], August. http://arxiv.org/abs/2008.04792.