Almost Sure Scattering for the Energy-Critical NLS with Radial Data Below H¹(ℝ⁴)
Abstract
We prove almost sure global existence and scattering for the energy-critical nonlinear Schrödinger equation with randomized spherically symmetric initial data in Hs(ℝ4) with 5/6 < s < 1. We were inspired to consider this problem by the recent work of Dodson-Lührmann-Mendelson, which treated the analogous problem for the energy-critical wave equation.
Recommended Citation
R. Killip et al., "Almost Sure Scattering for the Energy-Critical NLS with Radial Data Below H¹(ℝ⁴)," Communications in Partial Differential Equations, vol. 44, no. 1, pp. 51 - 71, Taylor & Francis, Jan 2019.
The definitive version is available at https://doi.org/10.1080/03605302.2018.1541904
Department(s)
Mathematics and Statistics
Keywords and Phrases
Almost sure scattering; Energy-critical NLS; Supercritical data
International Standard Serial Number (ISSN)
0360-5302; 1532-4133
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2019 Taylor & Francis, All rights reserved.
Publication Date
01 Jan 2019
Comments
R. K. was supported by NSF grant DMS-1600942. J. M. was supported in part by NSF DMS-1400706. M. V. was supported by NSF grant DMS-1500707.