Almost global existence for a fractional Schrödinger equation on spheres and tori - Archive ouverte HAL
Article Dans Une Revue Dynamics of Partial Differential Equations Année : 2013

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

Résumé

We study the time of existence of the solutions of the following Schr\"odinger equation $$i\psi_t = (-\Delta)^s \psi +f(|\psi|^2)\psi, x \in \mathbb S^d, or x\in\T^d$$ where $(-\Delta)^s$ 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 $s>1/2$.

Dates et versions

hal-01338763 , version 1 (29-06-2016)

Identifiants

Citer

Dario Bambusi, Yannick Sire. Almost global existence for a fractional Schrödinger equation on spheres and tori. Dynamics of Partial Differential Equations, 2013, 10 (2), pp.171--176. ⟨10.4310/DPDE.2013.v10.n2.a3⟩. ⟨hal-01338763⟩
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