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; He, Huijun; and Qiao, Zhijun, "LOCAL WELL-POSEDNESS AND BLOW-UP FOR A FAMILY OF U(1)-INVARIANT PEAKON EQUATIONS" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 75.