article published yes E Ryckman author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca 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 ℝ×ℝ4. 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. Johns Hopkins University Press2007 eng 1080-6377 math/050146210.1353/ajm.2007.0004 12911-60 yes Ryckman, E., and Monica Vişan. “Global Well-Posedness and Scattering for the Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” <i>American Journal of Mathematics</i>, vol. 129, no. 1, Johns Hopkins University Press, 2007, pp. 1–60, doi:<a href="https://doi.org/10.1353/ajm.2007.0004">10.1353/ajm.2007.0004</a>. Ryckman E, Vişan M. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. <i>American Journal of Mathematics</i>. 2007;129(1):1-60. doi:<a href="https://doi.org/10.1353/ajm.2007.0004">10.1353/ajm.2007.0004</a> E. Ryckman, M. Vişan, American Journal of Mathematics 129 (2007) 1–60. Ryckman, E., &#38; Vişan, M. (2007). Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. <i>American Journal of Mathematics</i>. Johns Hopkins University Press. <a href="https://doi.org/10.1353/ajm.2007.0004">https://doi.org/10.1353/ajm.2007.0004</a> Ryckman, E, and Monica Vişan. “Global Well-Posedness and Scattering for the Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” <i>American Journal of Mathematics</i>. Johns Hopkins University Press, 2007. <a href="https://doi.org/10.1353/ajm.2007.0004">https://doi.org/10.1353/ajm.2007.0004</a>. 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. E. Ryckman and M. Vişan, “Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4,” <i>American Journal of Mathematics</i>, vol. 129, no. 1. Johns Hopkins University Press, pp. 1–60, 2007. 220572026-06-19T07:57:32Z2026-06-29T10:30:01Z