Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms

Abstract

In this paper we consider the cubic Schrödinger 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>\frac{131}{416} $. We also obtain improved growth bounds for higher order Sobolev norms.