Blow-up criteria for fractional nonlinear Schrödinger equations. (August 2019) - Dinh, Van Duong
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.