Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures

Tayeb Aïssiou, Dmitry Jakobson, Fabricio Macià

We establish uniform bounds for the solutions $e^{it\Delta }u$ of the Schrödinger equation on arithmetic flat tori, generalising earlier results by J. Bourgain. We also study the regular…