Almost Sure Scattering for the Energy-Critical NLS with Radial Data Below H¹(ℝ⁴)
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.
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
Mathematics and Statistics
Keywords and Phrases
Almost sure scattering; Energy-critical NLS; Supercritical data
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2019