Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
Ryckman E, Vişan M. 2007. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. American Journal of Mathematics. 129(1), 1–60.
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Author
Ryckman, E;
Vişan, MonicaISTA
Abstract
We obtain global well-posedness, scattering, uniform regularity, and global L6t,x spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in âÃâ4. Our arguments closely follow those of Colliander, Keel, et al., though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the L6t,x-norm.
Publishing Year
Date Published
2007-02-01
Journal Title
American Journal of Mathematics
Publisher
Johns Hopkins University Press
Volume
129
Issue
1
Page
1-60
eISSN
IST-REx-ID
Cite this
Ryckman E, Vişan M. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. American Journal of Mathematics. 2007;129(1):1-60. doi:10.1353/ajm.2007.0004
Ryckman, E., & Vişan, M. (2007). Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. American Journal of Mathematics. Johns Hopkins University Press. https://doi.org/10.1353/ajm.2007.0004
Ryckman, E, and Monica Vişan. “Global Well-Posedness and Scattering for the Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” American Journal of Mathematics. Johns Hopkins University Press, 2007. https://doi.org/10.1353/ajm.2007.0004.
E. Ryckman and M. Vişan, “Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4,” American Journal of Mathematics, vol. 129, no. 1. Johns Hopkins University Press, pp. 1–60, 2007.
Ryckman E, Vişan M. 2007. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. American Journal of Mathematics. 129(1), 1–60.
Ryckman, E., and Monica Vişan. “Global Well-Posedness and Scattering for the Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” American Journal of Mathematics, vol. 129, no. 1, Johns Hopkins University Press, 2007, pp. 1–60, doi:10.1353/ajm.2007.0004.
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