Publications

Science Storms the Cloud

Chelle Leigh Gentemann, Chris Holdgraf, Ryan Abernathey, Daniel Crichton, James Colliander, Edward Joseph Kearns, Yuvi Panda, Richard P. Signell

System And Method For Enabling Crowd-sourced Examination Marking

Colliander James

Interaction Morawetz estimate for the magnetic Schrödinger equation and applications

James Colliander, Magdalena Czubak, Jeonghun J. Lee

Lower bound for the rate of blow-up of singular solutions of the Zakharov system in $\Bbb{R}^3$

James Colliander

Behavior of a Model Dynamical System with Applications to Weak Turbulence

James Colliander

Almost sure well-posedness of the cubic nonlinear Schrödinger equation below $L^2(\Bbb T)$

James Colliander, Tadahiro Oh

A remark on normal forms and the "upside-down" $I$-method for periodic NLS: Growth of higher Sobolev norms

James Colliander, Soonsik Kwon, Tadahiro Oh

Bootstrapped Morawetz estimates and resonant decomposition for low regularity global solutions of cubic NLS on $\Bbb{R}^2$

James Colliander, Tristan Roy

Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Remarks on global a priori estimates for the nonlinear Schrödinger equation

J. Colliander, M. Grillakis, N. Tzirakis

Numerical simulations of the energy-supercritical nonlinear Schrödinger equation

J. Colliander, G. Simpson, C. Sulem

Tensor products and correlation estimates with applications to nonlinear Schrödinger equations

J. Colliander, M. Grillakis, N. Tzirakis

Rough blowup solutions to the $L^2$ critical NLS

James Colliander, Pierre Raphaël

Energy critical NLS in two space dimensions

J. Colliander, S. Ibrahim, M. Majdoub, N. Masmoudi

Weighted low-regularity solutions of the KP-I initial-value problem

J. Colliander, A. D. Ionescu, C. E. Kenig, G. Staffilani

Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\Bbb{R}^2$

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems

James Colliander, Justin Holmer, Nikolaos Tzirakis

Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in $\Bbb{R}^3$

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $\Bbb{R}$

James Colliander, Justin Holmer, Monica Visan, Xiaoyi Zhang

A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order

Michael Christ, James Colliander, Terence Tao

The energy-critical nonlinear Schrödinger equation in $\Bbb{R}^3$

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

On blowup solutions of NLS with low regularity initial data

J. Colliander

Mass concentration window size and Strichartz norm divergence rate for the $L^2$-critical nonlinear Schrödinger equation

James Colliander, Svetlana Roudenko

Improved interaction Morawetz inequalities for the cubic nonlinear Schrödinger equation on $\Bbb{R}^2$

James Colliander, Manoussos Grillakis, Nikolaos Tzirakis

Errata to: ``Low regularity solutions for the Kadomtsev-Petviashvili I equation'' [Geom. Funct. Anal. bf 13 (2003), no. 4, 737--794; MR2006556]

James Colliander, Carlos E. Kenig, Gigliola Staffilani

Global well-posedness in Sobolev space implies global existence for weighted $L^2$ initial data for $L^2$-critical NLS

P. Blue, J. Colliander

Symplectic nonsqueezing of the Korteweg-de Vries flow

James Colliander, Markus Keel, Gigliola Staffilani, Hideo Takaoka, Terence Tao

Notes on symplectic non-squeezing of the KdV flow

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Ground state mass concentration in the $L^2$-critical nonlinear Schrödinger equation below $H^1$

J. Colliander, S. Raynor, C. Sulem, J. D. Wright

Multilinear estimates for periodic KdV equations, and applications

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $\Bbb{R}^3$

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Errata: ``On solutions for the Kadomtsev-Petviashvili I equation'' [Mosc. Math. J. bf 1 (2001), no. 4, 491--520, 644; MR1901072]

J. Colliander, C. E. Kenig, G. Staffilani

Sharp global well-posedness for KdV and modified KdV on $\Bbb{R}$ and $\Bbb{T}$

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Low regularity solutions for the Kadomtsev-Petviashvili I equation

J. Colliander, C. Kenig, G. Staffilani

Local well-posedness for dispersion-generalized Benjamin-Ono equations

J. Colliander, C. Kenig, G. Staffilani

Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations

Michael Christ, James Colliander, Terrence Tao

The generalized Korteweg-de Vries equation on the half line

J. E. Colliander, C. E. Kenig

Regularity bounds on Zakharov system evolutions

James Colliander, Gigliola Staffilani

Existence globale et diffusion pour l'équation de Schrödinger nonlinéaire répulsive cubique sur $\Bbb{R}^3$ en dessous l'espace d'énergie

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

A refined global well-posedness result for Schrödinger equations with derivative

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

On solutions for the Kadomtsev-Petviashvili I equation

J. Colliander, C. Kenig, G. Staffilani

Global well-posedness for Schrödinger equations with derivative

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Global well-posedness for KdV in Sobolev spaces of negative index

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Bilinear estimates and applications to 2D NLS

J. E. Colliander, J.-M. Delort, C. E. Kenig, G. Staffilani

Global wellposedness for KdV below $L^2$

J. Colliander, G. Staffilani, H. Takaoka

Ginzburg-Landau vortices: weak stability and Schrödinger equation dynamics

J. E. Colliander, R. L. Jerrard

Wellposedness for Zakharov systems with generalized nonlinearity

J. Colliander

Vortex dynamics for the Ginzburg-Landau-Schrödinger equation

J. E. Colliander, R. L. Jerrard

The initial value problem for the Zakharov system

James Ellis Colliander

On wellposedness of the Zakharov system

J. Bourgain, J. Colliander

Globalizing estimates for the periodic KPI equation

James E. Colliander

Thermal noise spectrum of a fiber-optic magnetostrictive transducer

F. Bucholtz, J. E. Colliander, A. Dandridge