Profile decompositions of fractional Schr\"odinger equations with   angularly regular data
  We study the fractional Schr\"odinger equations in $\mathbb R^{1+d}, d \geq 3$ of order ${d}/({d-1}) < \al < 2$. Under the angular regularity assumption we prove linear and nonlinear profile decompositions which extend the previous results \cite{chkl2} to data without radial assumption. As applications we show blowup phenomena of solutions to mass-critical fractional Hartree equations. 
Yonggeun Cho, Gyeongha Hwang, Soonsik Kwon and Sanghyuk Lee
math.AP