Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori

Abstract

We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.

28 pages

References in corpus (1)

• On integer solutions of Parsell-Vinogradov systems

Cited by in corpus (3)

• Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori
• Modified scattering for the cubic Schrödinger equation on Diophantine waveguides
• $l^2$ decoupling theorem for surfaces in ${\mathbb{R}}^3$