Blow-up of cylindrically symmetric solutions for Fractional NLS

In this paper, we consider blow-up of solutions to the Cauchy problem for the following fractional NLS, i \, ∂ₜ u=(-Δ)ˢ u-|u|2 σ u in \,\, × N, where N ≥ 2, $1/2 <s<1$ and 0<σ<2s/(N-2s). In the mass critical and supercritical cases, we establish a criterion for blow-up of solutions to the problem for cylindrically symmetric data. And we establish the existence of finite time blow-up solutions in the mass supercritical case. The results extend the known ones with respect to blow-up of solutions to the problem for radially symmetric data.