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We study, under the radial symmetry assumption, the solutions to thefractional Schr\"odinger equations of critical nonlinearity in $\mathbbR^{1+d}, d \geq 2$, with L\'{e}vy index ${2d}/({2d-1}) < \al < 2$. We firstlyprove the linear profile decomposition and then apply it to investigate theproperties of the blowup solutions of the nonlinear equations withmass-critical Hartree type nonlineartity.

Profile decompositions and Blowup phenomena of mass critical fractional Schr\"odinger equations