GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION

• 作 者: 杨凌燕 李晓光 吴永洪 Louis CACCETTA
• 机 构: SichuanNormalUniversity,WuhanInstituteofPhysicsandMachematicsChineseAcademyofScience,DepartmentofMat
• 出 处: 数学物理学报：B辑英文版
• 发表日期: 2017年4期
• 关键词: 整体适定性 方程 爆破 柯西问题 整体存在 二分法 SC 基态 Hartree equation Threshold criteria blow-up solu
• 基金项目: This work was supported by the National Natural Science Foundation of China （11371267） and Sichuan Province Science Foundation for Youths （2012JQ0011）.

For 2 < γ < min{4, n}, we consider the focusing Hartree equation iu_t+ △u +(|x|~(-γ)* |u|~2)u = 0, x ∈ R~n.(0.1)Let M [u] and E [u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of-△ Q + Q =(|x|~(-γ)* |Q|~2)Q.