@article{22067,
  abstract     = {We consider the derivative nonlinear Schrödinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and L^2-critical with respect to scaling. We first discuss whether ensembles of orbits with L^2-equicontinuous initial data remain equicontinuous under evolution. We prove that this is true under the restriction 
M(q)=∫∣∣q∣∣2<4π. We conjecture that this restriction is unnecessary. Further, we prove that the problem is globally well posed for initial data in H1∕6 under the same restriction on M. Moreover, we show that this restriction would be removed by a successful resolution of our equicontinuity conjecture.},
  author       = {Killip, Rowan and Ntekoume, Maria and Visan, Monica},
  issn         = {1948-206X},
  journal      = {Analysis & PDE},
  number       = {5},
  pages        = {1245--1270},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{On the well-posedness problem for the derivativenonlinear Schrödinger equation}},
  doi          = {10.2140/apde.2023.16.1245},
  volume       = {16},
  year         = {2023},
}