Almost sure scattering at mass regularity for radial Schrödinger equations. (7th September 2022)

• Record Type: Journal Article
• Authors: Latocca, Mickaël
• Is Part Of: Nonlinearity. Volume 35:Number 10(2022)
• Page Start: 5311
• Page End: 5356
• Publication Date: 2022-09-07
• Subjects: dispersive -- random-data -- scattering -- nonlinear-schrodinger; 35L05 -- 35L15 -- 35L71; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac8aed
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the radial nonlinear Schrödinger equation i ∂ t u + Δ u = | u | p −1 u in dimension d ⩾ 2 for p ∈ 1, 1 + 4 d and construct a natural Gaussian measure μ 0 which support is almost L rad 2 and such that μ 0 —almost every initial data gives rise to a unique global solution. Furthermore, for p > 1 + 2 d and d ⩽ 10, the solutions constructed scatter in a space which is almost L 2 . This paper can be viewed as a higher dimensional counterpart of the work of Burq and Thomann (2020 arXiv:2012.13571 ), in the radial case.