51 citations · 54 across the 7 of their papers we have counts for
17 papers · 1 filter
Symplectic nonsqueezing of the KdV flow
J. Colliander, M. Keel, G. Staffilani +2
We prove two finite dimensional approximation results and a symplectic non-squeezing property for the Korteweg-de Vries (KdV) flow on the circle T. The nonsqueezing result relies o…
Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3
Jim Colliander, Mark Keel, Gigliola Staffilani +2
We obtain global well-posedness, scattering, and global spacetime bounds for energy-class solutions to the quintic defocusing Schrödinger equation in , whi…
Stability of Solitons for the KdV equation in H^s, 0 <= s< 1
S. Raynor, G. Staffilani
We study the long-time stability of soliton solutions to the Korteweg-deVries equation. We consider solutions to the KdV with initial data in , , that are in…
Global existence and scattering for rough solutions of a nonlinear Schroedinger equation on R^3
J. Colliander, M. Keel, G. Staffilani +2
We prove global existence and scattering for the defocusing, cubic nonlinear Schrödinger equation in $H^s(\rr^3)$ for . The main new estimate in the argument is a Morawe…
Polynomial upper bounds for the instability of the Nonlinear Schrödinger equation below the energy norm
J. Colliander, M. Keel, G. Staffilani +2
We continue the study (initiated in \cite{ckstt:7}) of the orbital stability of the ground state cylinder for focussing non-linear Schrödinger equations in the norm for…
Local well-posedness for dispersion generalized Benjamin-Ono equations
J. Colliander, C. Kenig, G. Staffilani
In this paper we study local well-posedness in the energy space for a family of dispersive equations that can be seen as dispersive ``interpolations'' between the KdV and the Benja…