Growth of solutions to NLS on irrational tori

TL;DR

This paper establishes polynomial bounds on the growth of higher Sobolev norms for the nonlinear Schrödinger equation on irrational tori in three dimensions, leveraging improved Strichartz estimates to achieve better results than on rational tori.

Contribution

It provides new polynomial bounds for Sobolev norm growth on irrational tori, improving upon previous results by utilizing enhanced Strichartz estimates.

Findings

Polynomial bounds on Sobolev norm growth in 3D NLS

Better bounds for irrational tori compared to rational tori

Utilization of improved Strichartz estimates

Abstract

We prove polynomial bounds on the growth of higher Sobolev norms for the nonlinear Schrodinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearity. Due to improved Strichartz estimates, these bounds are better for irrational tori than they are for rational tori.