Profile decompositions and blowup phenomena of mass critical fractional Schrödinger equations

We study, under the radial symmetry assumption, the solutions to the fractional Schrödinger equations of critical nonlinearity in R1+d,d≥2R1+d,d≥2, with Lévy index 2d/(2d−1)<α<22d/(2d−1)<α<2. We first prove the linear profile decomposition and then apply it to investigate the properties of the blowup solutions of the nonlinear equations with mass-critical Hartree type nonlinearity.