Local Well-posedness for 2-D Schrodinger Equation on Irrational Tori and Bounds on Sobolev Norms

TL;DR

This paper improves Strichartz estimates for the 2D cubic Schrödinger equation on irrational tori, establishing local well-posedness for s>131/416 and providing better bounds on Sobolev norm growth.

Contribution

It introduces enhanced Strichartz estimates on irrational tori and applies them to prove local well-posedness and Sobolev norm bounds.

Findings

Improved Strichartz estimates for irrational tori

Local well-posedness in H^s for s>131/416

Enhanced bounds on Sobolev norm growth

Abstract

In this paper we consider the cubic Schrodinger equation in two space dimensions on irrational tori. Our main result is an improvement of the Strichartz estimates on irrational tori. Using this estimate we obtain a local well-posedness result in H^s for s>131/416. We also obtain improved growth bounds for higher order Sobolev norms.