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

作     者：杨凌燕 李晓光 吴永洪 Louis CACCETTA 

作者机构：Sichuan Normal UniversityChengdu610066China Wuhan Institute of Physics and Machematics Chinese Academy of ScienceWuhan 430071China Department of Mathematics and StatisticsCurtin University of TechnologyPerthWA 6845Australia 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2017年第37卷第4期

页      面：941-948页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(11371267) Sichuan Province Science Foundation for Youths(2012JQ0011) 

主　　题：Hartree equation Threshold criteria blow-up solution 

摘      要：For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut ＋ Au ＋ （｜x｜^-γ ＊ ｜u｜2）u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ ＋ Q = （｜x｜^-γ ＊ ｜Q｜^2）Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of （0,1） if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^（sc= r-2/2）. In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation （0.1）.