51 citations · 54 across the 6 of their papers we have counts for
12 papers · 1 filter
Global wellposedness of the modified Benjamin-Ono equation with initial data in
Carlos E. Kenig, Hideo Takaoka
We prove that the modified Benjamin-Ono equation is globally wellposed in for .
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…
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…
Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm
Jim Colliander, Mark Keel, Gigliola Staffilani +2
We study the long-time behaviour of the focusing cubic NLS on in the Sobolev norms for . We obtain polynomial growth-type upper bounds on the norms, and…