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

Dario Bambusi, Yannick Sire

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 $(-\Delta {)}^s$ stands for the sp…