ON THE BLOW-UP PHENOMENON FOR THE MASS-CRITICAL FOCUSING HARTREE EQUATION IN R-4

We characterize the dynamics of the finite time blow-up solutions with minimal mass for the focusing mass-critical Hartree equation with H-1(R-4) data and L-2(R-4) data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we analyze the mass concentration phenomenon of such blow-up solutions.