Energy Criteria Of Global Existence For The Hartree Equation With Coulomb Potential

The Hartree equation is a quantum mechanical equation first proposed by physicist Douglas Hartree in 1928.It’s a multi-electron theory used to describe the behavior of electrons in atomic and molecular systems.Nonlinear Hartree equations are a class of nonlinear Schr?dinger equations with nonlocal nonlinear terms.It can be considered as the classical limit of the field equations describing a quantum mechanical nonrelativistic many boson system.This thesis studies a class of nonlinear Hartree equations with Coulomb potential.Combined with the conservation of mass and energy,we analyze the variational characteristics of the corresponding nonlinear elliptic equation.According to the range of parameters,we construct the evolution invariant flows of the equation in different cases.Then the sharp energy thresholds for global existence and blow-up of solutions are discussed in detail.