51 citations · 87 across the 9 of their papers we have counts for
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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…
Global well-posedness for KdV in Sobolev Spaces of negative index
J. Colliander, M. Keel, G. Staffilani +2
The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial…