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

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 dicho...

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Bibliographic Details
Published in:Acta mathematica scientia 2017-07, Vol.37 (4), p.941-948
Main Author: 杨凌燕 李晓光 吴永洪 Louis CA CCETTA
Format: Article
Language:English
Subjects:
35J10
35Q55
blow-up solution
Hartree equation
Threshold criteria
二分法
基态
整体存在
整体适定性
方程
柯西问题
爆破
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Summary: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）.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(17)30049-8