Blow-up And Global Existence To Cauchy Problem For Nonlocal Schr(?)dinger Equation

This thesis considers the following nonlocal Schr(?)dinger equation(?)When 2 < ? < min{4, n}, n?3, ?=2, let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of stationary equation-? Q+Q=(|x|-?*|Q|2)Q. We obtain a criteria on blow-up and global existence for equation(P1) when (?)(? is a given constant,sc = ?-2/2).This result extends the conclusion drawn in the Gao, Wang[6](Z. Angew. Math. Phy.,Scattering versus blow-up for the focusing L2 supercritical Hartree equation: 179-202, 2014)in the case of (?). What is more, using Gagliardo-Nirenberg equality and the related mass conservation and energy conservation, we establish invariant evolution flows of the equation(Pl) when ? = 1,7/3??<5. On the basis of the invariant evolution flows, a sharp threshold of blow-up and global existence of the Cauchy problem is derived.