Blow-up criteria for fractional nonlinear Schrödinger equations

Abstract

We consider the focusing fractional nonlinear Schrödinger equation i∂tu−(−Δ)su=−|u|αu,(t,x)∈R+×Rd,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 L2-critical and L2-supercritical cases which extend the results of Boulenger–Himmelsbach–Lenzmann (Boulenger et al., 2016) for non-radial initial data.