Blow-up Dynamics for L2-Critical Fractional Schrödinger Equations

Abstract In this paper, we consider the L²-critical fractional Schrödinger equation iuₜ-|D|^ u+|u|^2 u=0 with initial data u₀ H^ /2 (R) and close to 2. We show that if the initial data have negative energy and slightly supercritical mass, then the solution blows up in finite time. We also give a specific description for the blow-up dynamics. This is an extension of the works of F. Merle and P. Raphaël for L²-critical Schrödinger equations. However, the nonlocal structure of this equation and the lack of some symmetries make the analysis more complicated, hence some new strategies are required.