Growth of higher Sobolev norms for energy critical NLS on irrational tori: small energy case

TL;DR

This paper proves polynomial bounds on higher Sobolev norms for small-energy solutions of the energy-critical nonlinear Schrödinger equation on irrational tori, advancing understanding of long-time solution behavior.

Contribution

It introduces new polynomial bounds for Sobolev norms of solutions on irrational tori, leveraging recent long-time Strichartz estimates.

Findings

Polynomial upper bounds for higher Sobolev norms

Applicable to solutions with small energy

Extends analysis to generic irrational tori

Abstract

We consider the energy critical nonlinear Schrodinger equation on generic irrational tori. Using the long-time Strichartz estimates proved in [8], we establish polynomial upper bounds for higher Sobolev norms for solutions with small energy.