most citedGlobal well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3

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math.AP2004★ 51 cited

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…

math.AP2001

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…

math.AP2001

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…