191 citations · 403 across the 17 of their papers we have counts for
17 papers
Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm
Markus Keel, Tristan Roy, Terence Tao
We show that the Maxwell-Klein-Gordon equations in three dimensions are globally well-posed in in the Coulomb gauge for all . This extends pre…
Weakly turbulent solutions for the cubic defocusing nonlinear Schrödinger equation
J. Colliander, M. Keel, G. Staffilani +2
We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to hig…
Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2
J. Colliander, M. Keel, G. Staffilani +2
The initial value problem for the cubic defocusing nonlinear Schrödinger equation on the plane is shown to be globally well-posed for initial data i…
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…
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…