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arXiv · 2010.07131

Remarks on the fractional inhomogeneous Hartree equation

Tarek Saanouni
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Abstract

This paper studies the inhomogeneous fractional Schödinger equation $$i\dot u-(-Δ)^s u=\pm(I_α*|\cdot|^b|u|^p)|x|^b|u|^{p-2}u.$$ In the mass super-critical and energy sub-critical regimes, using a Gagliardo-Nirenberg adapted to the above problem, the standing waves give a sharp threshold of global existence versus finite time blow-up of solutions.

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Tarek Saanouni. 2020-10-14. Remarks on the fractional inhomogeneous Hartree equation. https://arxiv.org/abs/2010.07131

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