51 citations · 98 across the 16 of their papers we have counts for
7 papers · 2 filters
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…
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…
Low regularity solutions for the Kadomtsev-Petviashvili I equation
J. Colliander, C. Kenig, G. Staffilani
In this paper we obtain local in time existence and (suitable) uniqueness and continuous dependence for the KP-I equation for small data in the intersection of the energy space and…
KdV and Almost Conservation Laws
Gigliola Staffilani
This short survey paper is concerned with a new method to prove global well-posedness results for dispersive equations below energy spaces, namely for the Schrödinger equat…
Almost conservation laws and global rough solutions to a Nonlinear Schrödinger equation
J. Colliander, M. Keel, G. Staffilani +2
We prove an "almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in H^s(R^n) when n = 2, 3 and s > 4/7, 5/6,…