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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
Affiliation:
Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756, Republic of Korea, (changocho@jbnu.ac.kr)
Gyeongha Hwang*
Affiliation:
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 689-798, Republic of Korea, (ghhwang@unist.ac.kr)
Soonsik Kwon
Affiliation:
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea, (soonsikk@kaist.edu)
Sanghyuk Lee
Affiliation:
Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea, (shklee@snu.ac.kr)
*
*Corresponding author

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
Copyright
Copyright © Royal Society of Edinburgh 2015 

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