Almost sure scattering for the energy-critical NLS with radial data below H1(R4). Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Killip, Rowan; Murphy, Jason; Visan, Monica
• Is Part Of: Communications in partial differential equations. Volume 44:Issue 1(2019)
• Page Start: 51
• Page End: 71
• Publication Date: 2019-01-02
• Subjects: Almost sure scattering -- energy-critical NLS -- supercritical data; 35Q55; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2018.1541904
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: We prove almost sure global existence and scattering for the energy-critical nonlinear Schrödinger equation with randomized spherically symmetric initial data inH s ( R 4 ) with5 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.