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A note on the fractional Schrödinger equation of Choquard type
Journal article   Open access  Peer reviewed

A note on the fractional Schrödinger equation of Choquard type

Tarek Saanouni
Journal of mathematical analysis and applications, Vol.470(2), pp.1004-1029
15/02/2019
DOI: https://doi.org/10.1016/j.jmaa.2018.10.045

Abstract

Blow-up Gagliardo–Nirenberg inequality Global existence Nonlinear fractional Schrödinger–Choquard equation
Some well-posedness issues for a class of fractional Schrödinger–Choquard equations are investigated. First, local well-posedness is obtained in the energy space. Second, the best constant of a Gagliardo–Nirenberg type inequality is investigated. Third, a sharp threshold of global existence versus blow-up dichotomy is obtained. Finally, the mass concentration is established for the blowing-up solutions of the mass critical equation.
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https://doi.org/10.1016/j.jmaa.2018.10.045View
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