191 citations · 878 across the 41 of their papers we have counts for
4 papers · 2 filters
A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
Michael Christ, James Colliander, Terence Tao
Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces , for negative but close to 0.…
Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on
J. Colliander, J. Holmer, M. Visan +1
We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness a…
A remark on the concentration phenomenon for the L^2-critical nonlinear Schrodinger equations
James Colliander, Svetlana Roudenko
We observe a link between the window size of mass concentration and the rate of explosion of the Strichartz norm by revisiting Bourgain's mass concentration for the L^2-critical no…
Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems
Jim Colliander, Justin Holmer, Nikolaos Tzirakis
We prove low-regularity global well-posedness for the 1d Zakharov system and 3d Klein-Gordon-Schrödinger system, which are systems in two variables $u:\mathbb{R}_x^d\times \mathbb{…