Blow-up criteria for fractional nonlinear Schrödinger equations. (August 2019)

• Record Type: Journal Article
• Authors: Dinh, Van Duong
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 117
• Page End: 140
• Publication Date: 2019-08
• Subjects: Fractional nonlinear Schrödinger equation -- Local well-posedness -- Virial estimates -- Blow-up criteria; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider the focusing fractional nonlinear Schrödinger equation i ∂ t u − ( − Δ ) s u = − | u | α u, ( t, x ) ∈ R + × R d, where s ∈ ( 1 ∕ 2, 1 ) and α > 0 . By using localized virial estimates, we establish general blow-up criteria for non-radial solutions to the equation. As consequences, we obtain blow-up criteria in both L 2 -critical and L 2 -supercritical cases which extend the results of Boulenger–Himmelsbach–Lenzmann (Boulenger et al., 2016) for non-radial initial data.