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On finite time blow-up for the mass-critical Hartree equations

Published online by Cambridge University Press:  03 June 2015

Yonggeun Cho ,
Gyeongha Hwang ,
Soonsik Kwon  and
Sanghyuk Lee
Yonggeun Cho
Affiliation:
Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756, Republic of Korea, ([email protected])
Gyeongha Hwang*
Affiliation:
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 689-798, Republic of Korea, ([email protected])
Soonsik Kwon
Affiliation:
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea, ([email protected])
Sanghyuk Lee
Affiliation:
Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea, ([email protected])
*
*Corresponding author
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Abstract

We consider the fractional Schrödinger equations with focusing Hartree-type nonlinearities. When the energy is negative, we show that the solution blows up in a finite time. For this purpose, based on Glassey’s argument, we obtain a virial-type inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 3 , June 2015 , pp. 467 - 479
Copyright
Copyright © Royal Society of Edinburgh 2015 

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