Search Results - "Colliander, James"

Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems by Colliander, James, Holmer, Justin, Tzirakis, Nikolaos

“…We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables…”
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Asymptotics, Frequency Modulation, and Low Regularity Ill-Posedness for Canonical Defocusing Equations by Christ, Michael, Colliander, James, Tao, Terrence

“…In a recent paper, Kenig, Ponce and Vega study the low regularity behavior of the focusing nonlinear Schrödinger (NLS), focusing modified Korteweg-de Vries…”
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A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order by Christ, Michael, Colliander, James, Tao, Terence

“…Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces H s , for s…”
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Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L2(T) by Colliander, James, Oh, Tadahiro

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How open data and interdisciplinary collaboration improve our understanding of space weather: A risk and resiliency perspective by Ledvina, Vincent E., Palmerio, Erika, McGranaghan, Ryan M., Halford, Alexa J., Thayer, Aidan, Brandt, Laura, MacDonald, Elizabeth A., Bhaskar, Ankush, Dong, Chuanfei, Altintas, Ilkay, Colliander, James, Jin, Meng, Jain, Richa N., Chatterjee, Subhamoy, Shaikh, Zubair, Frissell, Nathaniel A., Chen, Thomas Y., French, Ryan J., Isola, Brianna, McIntosh, Scott W., Mason, Emily I., Riley, Pete, Young, Tim, Barkhouse, Wayne, Kazachenko, Maria D., Snow, Martin, Ozturk, Dogacan S., Claudepierre, Seth G., Di Mare, Francesca, Witteman, Andy, Kuzub, Jeremy

“…Space weather refers to conditions around a star, like our Sun, and its interplanetary space that may affect space- and ground-based assets as well as human…”
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Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L 2 ( T ) by Colliander, James, Oh, Tadahiro

“…We consider the Cauchy problem for the 1-dimensional periodic cubic nonlinear Schrödinger (NLS) equation with initial data below L 2 . In particular, we…”
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A remark on normal forms and the “upside-down” I-method for periodic NLS: Growth of higher Sobolev norms by Colliander, James, Kwon, Soonsik, Oh, Tadahiro

“…We study growth of higher Sobolev norms of solutions of the onedimensional periodic nonlinear Schrödinger equation (NLS). By a combination of the normal form…”
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Regularity bounds on Zakharov system evolutions by James Colliander, Gigliola Staffilani

“…Spatial regularity properties of certain global-in-time solutions of the Zakharov system are established. In particular, the evolving solution $u(t)$ is shown…”
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Tensor products and correlation estimates with applications to nonlinear Schrödinger equations by Colliander, James, Tzirakis, Nikolaos, Grillakis, Manoussos G.

“…We prove new interaction Morawetz‐type (correlation) estimates in one and two dimensions. In dimension 2 the estimate corresponds to the nonlinear diagonal…”
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Behavior of a Model Dynamical System with Applications to Weak Turbulence by Colliander, James E., Marzuola, Jeremy L., Oh, Tadahiro, Simpson, Gideon

“…We experimentally explore solutions to a model Hamiltonian dynamical system recently derived to study frequency cascades in the cubic defocusing nonlinear…”
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Rough blowup solutions to the L2 critical NLS by Colliander, James, Raphaël, Pierre

“…We study the singularity formation for the cubic focusing L 2 -critical nonlinear Schrödinger equation on . In a series of recent works, Merle and Raphaël have…”
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Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^{2}(\mathbb{T}) by Colliander, James, Oh, Tadahiro

“…We consider the Cauchy problem for the 1-dimensional periodic cubic nonlinear Schrödinger (NLS) equation with initial data below L^{2} . In particular, we…”
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Rough blowup solutions to the L 2 critical NLS by Colliander, James, Raphaël, Pierre

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Symplectic nonsqueezing of the korteweg-de vries flow by Colliander, James, Staffilani, Gigliola, Keel, Markus, Takaoka, Hideo, Tao, Terence

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Global well-posedness and scattering for the energy-critical Schrödinger equation in ℝ 3 by Colliander, James, Keel, Markus, Staffilani, Gigliola, Takaoka, Hideo, Tao, Terence

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The Visualization, Exploration, and Data Analysis (VEDA) Platform: A Modular, Open Platform Lowering the Barrier to entry to Cloud Computing by Freitag, Brian M., Maskey, Manil, Barciauskas, Aimee, Solvsteen, Jonas, Colliander, James, Munroe, James

“…Increasing data volumes and migration of data to the cloud introduces challenges related to scalability and complexity to users of National Aeronautics and…”
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Errata to “Low Regularity Solutions for the Kadomtsev–Petviashvili I Equation”, GAFA, Geom. Funct. Anal. 13 (2003), 737-794 by Colliander, James, Kenig, Carlos E., Staffilani, Gigliola

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Improved Interaction Morawetz Inequalities for the Cubic Nonlinear Schrödinger Equation on ℝ2 by Colliander, James, Grillakis, Manoussos, Tzirakis, Nikolaos

“…We prove global well-posedness for low regularity data for the L2-critical defocusing nonlinear Schrödinger equation (NLS) in 2D. More precisely, we show that…”
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Almost sure well-posedness of the cubic nonlinear Schr\"odinger equation below L^2(T) by Colliander, James, Oh, Tadahiro

“…Duke Math. J. 161, no. 3 (2012), 367-414 We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear Schr\"odinger equation (NLS) with…”
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Interaction Morawetz estimate for the magnetic Schr\"odinger equation and applications by Colliander, James, Czubak, Magdalena, Lee, Jeonghun

“…We establish an interaction Morawetz estimate for the magnetic Schr\"odinger equation for $n\geq 3$ under certain smallness conditions on the gauge potentials,…”
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