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arXiv · 1301.2062

Almost global existence for a fractional Schrodinger equation on spheres and tori

Dario Bambusi·Yannick Sire
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Abstract

We study the time of existence of the solutions of the following Schrödinger equation $$iψ_t = (-Δ)^s ψ+f(|ψ|^2)ψ, x \in \mathbb S^d, or x\in\T^d$$ where $(-Δ)^s$ stands for the spectrally defined fractional Laplacian with $s>1/2$ and $f$ a smooth function. We prove an almost global existence result for almost all $s>1/2$.

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Dario Bambusi, Yannick Sire. 2013-01-10. Almost global existence for a fractional Schrodinger equation on spheres and tori. https://arxiv.org/abs/1301.2062

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