119 citations · 209 across the 10 of their papers we have counts for
7 papers · 2 filters
On solutions for the Kadomtsev-Petviashvili I equation
J. Colliander, C. Kenig, G. Staffilani
Oscillatory integral techniques are used to study the well-posedness of the KP-I equation for initial data that are small with respect to the norm of a weighted Sobolev space invol…
The generalized Korteweg-de Vries equation on the half line
J. E. Colliander, C. E. Kenig
The initial-boundary value problem for the generalized Korteweg-de Vries equation on a half-line is studied by adapting the initial value techniques developed by Kenig, Ponce and V…
Sharp Global well-posedness for KdV and modified KdV on and $\T$
J. Colliander, M. Keel, G. Staffilani +2
The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value pro…
Multilinear estimates for periodic KdV equations and applications
Jim Colliander, Markus Keel, Gigliola Staffilani +2
We prove an endpoint multilinear estimate for the spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for perio…
A refined global well-posedness result for Schrodinger equations with derivative
J. Colliander, M. Keel, G. Staffilani +2
In this paper we prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in , for for data small in . To under…
Global well-posedness for Schrödinger equations with derivative
J. Colliander, M. Keel, G. Staffilani +2
We prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in , for for small data. The result follows from an ap…