@article{22088,
  abstract     = {We consider the focusing cubic nonlinear Schrödinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS. We also prove failure of uniform space-time bounds at the threshold.},
  author       = {Killip, Rowan and Murphy, Jason and Visan, Monica and Zheng, Jiqiang},
  issn         = {0893-4983},
  journal      = {Differential and Integral Equations},
  number       = {3/4},
  pages        = {161--206},
  publisher    = {Khayyam Publishing},
  title        = {{The focusing cubic NLS with inverse-square potential in three space dimensions}},
  doi          = {10.57262/die/1487386822},
  volume       = {30},
  year         = {2017},
}

@article{22085,
  abstract     = {We prove global well posedness and scattering for the nonlinear Schröodinger equation with power-type nonlinearity (mathematical formular) below the energy space, i.e., for s<1. In [15], J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao established polynomial growth of the 
Hs/x-norm of the solution, and hence global well posedness for initial data in Hs/x, provided 
s is sufficiently close to 1. However, their bounds are insufficient to yield scattering. In this paper, we use the a priori interaction Morawetz inequality to show that scattering holds in H^s(R^n)
 whenever s is larger than some value 0<s0(n,p)<1.},
  author       = {Visan, Monica and Zhang, Xiaoyi},
  issn         = {0893-4983},
  journal      = {Differential and Integral Equations},
  number       = {1/2},
  pages        = {99--124},
  publisher    = {Khayyam Publishing},
  title        = {{Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space}},
  doi          = {10.57262/die/1356038556},
  volume       = {22},
  year         = {2009},
}