119 citations · 157 across the 4 of their papers we have counts for
7 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…
blowup solutions of cubic NLS on concentrate a fixed amount of mass
J. Colliander, W. Staubach
The authors have found an error in their argument, so this paper is withdrawn.
Instability of the periodic nonlinear Schrodinger equation
Michael Christ, James Colliander, Terence Tao
We study the periodic non-linear Schrodinger equations with odd integer power nonlinearities, for initial data which are assumed to be small in some negative order Sobolev space, b…
Ill-posedness for nonlinear Schrodinger and wave equations
Michael Christ, James Colliander, Terence Tao
The nonlinear wave and Schrodinger equations on Euclidean space of any dimension, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be…
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…