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Well-posedness and blow-up of Virial type for some fractional inhomogeneous Choquard equations
Journal article   Peer reviewed

Well-posedness and blow-up of Virial type for some fractional inhomogeneous Choquard equations

L. Chergui and Lassaad Chergui
Applicable analysis, Vol.101(8), pp.2966-2995
24/05/2022
DOI: https://doi.org/10.1080/00036811.2020.1834085

Abstract

blow-up Choquard equation Gagliardo-Nirenberg inequality ground state virial identity
In the subcritical energy case, local well-posedness is established in the radial energy space for a class of fractional inhomogeneous Choquard equations. The best constant of a Gagliardo-Nirenberg type inequality is obtained. Moreover, a sharp threshold of global existence versus blow-up dichotomy is obtained for mass super-critical and energy subcritical solutions.

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