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

被引：4
|
作者：
Yang, Lingyan [1 ]
Li, Xiaoguang [1 ,2 ]
Wu, Yonghong [3 ]
Caccetta, Louis [3 ]
机构：
[1] Sichuan Normal Univ, Chengdu 610066, Sichuan, Peoples R China
[2] Chinese Acad Sci, Wuhan Inst Phys & Machemat, Wuhan 430071, Hubei, Peoples R China
[3] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia
来源：
ACTA MATHEMATICA SCIENTIA | 2017年 / 37卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Hartree equation; Threshold criteria; blow-up solution; NONLINEAR SCHRODINGER; SCATTERING;
D O I：
10.1016/S0252-9602(17)30049-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For 2 < gamma < min{4, n}, we consider the focusing Hartree equation iu(t) Delta u + (vertical bar X vertical bar(-gamma) * vertical bar u vertical bar(2))u = 0, x is an element of 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 - Delta Q + Q = (vertical bar x1 vertical bar(-gamma) * vertical bar Q vertical bar(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](1-sc) E[u](sc) < M[Q](1-sc) E[Q](sc) (s(c) = gamma-2/2V). In this paper, we consider the complementary case M[u](1-sc) E[u](sc) >= M[Q](1-sc) E[Q](sc) and obtain a criteria on blow-up and global existence for the Hartree equation (0.1).
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页码：941 / 948
页数：8
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