Profile decompositions and blowup phenomena of mass critical fractional Schrodinger equations

Abstract

We study, under the radial symmetry assumption, the solutions to the fractional Schrodinger equations of critical nonlinearity in R1+d, d >= 2, with Levy index 2d/(2d - 1) < alpha < 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. (C) 2013 Elsevier Ltd. All rights reserved.