Uniform estimates for the solutions of the Schr "odinger equation on the\n torus and regularity of semiclassical measures

2011/10/29 by Dmitry Jakobson, Aïssiou, Tayeb, Jakobson, Dmitry +2 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1110.6521

openalex publication_date 2011/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish uniform bounds for the solutions e^it\Δu of the\nSchr "odinger equation on arithmetic flat tori, generalising earlier results\nby J. Bourgain. We also study the regularity properties of weak-* limits of\nsequences of densities of the form |e^it\Δu_n|² corresponding to\nhighly oscillating sequences of initial data (u_n). We obtain improved\nregularity properties of those limits using previous results by N. Anantharaman\nand F. Maci `a on the structure of semiclassical measures for solutions to the\nSchr "odinger equation on the torus.\n

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• Observability of Schrödinger propagators on tori in rough settings

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