@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},
}

@article{10738,
  abstract     = {We prove an adiabatic theorem for the Landau–Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fröhlich Hamiltonian with large coupling constant α. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau–Pekar equations until times short compared to α2.},
  author       = {Leopold, Nikolai K and Rademacher, Simone Anna Elvira and Schlein, Benjamin and Seiringer, Robert},
  issn         = {1948-206X},
  journal      = {Analysis and PDE},
  number       = {7},
  pages        = {2079--2100},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{The Landau–Pekar equations: Adiabatic theorem and accuracy}},
  doi          = {10.2140/APDE.2021.14.2079},
  volume       = {14},
  year         = {2021},
}

@article{22051,
  abstract     = {We construct solutions with prescribed scattering state to the cubic-quintic NLS (mathematical formular)in three spatial dimensions in the class of solutions with (mathematical formular). This models disturbances in an infinite expanse of (quantum) fluid in its quiescent state— the limiting modulus c corresponds to a local minimum in the energy density.
Our arguments build on work of Gustafson, Nakanishi, and Tsai on the (defocusing) Gross–Pitaevskii equation. The presence of an energy-critical nonlinearity and changes in the geometry of the energy
functional add several new complexities. One new ingredient in our argument is a demonstration that
solutions of such (perturbed) energy-critical equations exhibit continuous dependence on the initial data
with respect to the weak topology on H1/x.},
  author       = {Killip, Rowan and Murphy, Jason and Visan, Monica},
  issn         = {1948-206X},
  journal      = {Analysis & PDE},
  keywords     = {final-state problem, wave operators, cubic-quintic NLS, nonvanishing boundary conditions},
  number       = {7},
  pages        = {1523--1574},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions}},
  doi          = {10.2140/apde.2016.9.1523},
  volume       = {9},
  year         = {2016},
}

@article{22024,
  abstract     = {We revisit the proof of global well-posedness and scattering for the defocusing energy-critical NLS in three space dimensions in light of recent developments. This result was obtained previously by Colliander, Keel, Staffilani, Takaoka, and Tao.},
  author       = {Killip, Rowan and Visan, Monica},
  issn         = {1948-206X},
  journal      = {Analysis & PDE},
  keywords     = {energy critical, nonlinear Schrödinger},
  number       = {4},
  pages        = {855--885},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{Global well-posedness and scattering for the defocusing quintic NLS in three dimensions}},
  doi          = {10.2140/apde.2012.5.855},
  volume       = {5},
  year         = {2012},
}

@article{22082,
  abstract     = {We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation (mathematical formular)  for large spherically symmetric L2/x(R^d) initial data in dimensions d >= 3.
In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.},
  author       = {Killip, Rowan and Visan, Monica and Zhang, Xiaoyi},
  issn         = {1948-206X},
  journal      = {Analysis & PDE},
  number       = {2},
  pages        = {229--266},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher}},
  doi          = {10.2140/apde.2008.1.229},
  volume       = {1},
  year         = {2008},
}