Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (6): 1117-1123.

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A Sharp Threshold of Blow-Up of a Class of Schrödinger-Hartree Equations

Yang Lingyan, Li Xiaoguang, Chen Ying   

  1. School of Mathematics and VC & VR Province Key Lab, Sichuan Normal University, Chengdu 610068
  • Received:2016-03-25 Revised:2016-09-20 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the NSFC (11371267) and the National Science Foundation for Distinguished Young Scholars of Sichuan Province (2012JQ0011)

Abstract:

In this paper, the Schrödinger-Hartree equation
itψ+△ψ=-(|x|-1*|ψ|α)|ψ|α-2}ψ, t>0,x∈R3,α≥2 (P)
is considered in R3. We establish invariant evolution flows of the equation by Gagliardo-Nirenberg inequality, mass conservation and energy conservation of the equation (P). When (7)/(3)≤α < 5, a sharp threshold of global existence and blow-up of the Cauthy problem is derived.

Key words: Schrödinger-Hartree equation, Invariant evolution flows, Blow-up solution, Sharp threshold

CLC Number: 

  • O175.23
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