Long-time Strichartz estimates on 3D waveguide with applications

TL;DR

This paper develops long-time Strichartz estimates for the Schrödinger equation on 3D waveguides and applies them to bound Sobolev norm growth in nonlinear cases.

Contribution

It introduces new long-time Strichartz estimates specific to 3D waveguides and uses these to analyze Sobolev norm growth in nonlinear Schrödinger equations.

Findings

Established upper bounds on Sobolev norm growth

Extended Strichartz estimates to waveguide geometries

Provided tools for nonlinear Schrödinger analysis in waveguides

Abstract

We study long-time Strichartz estimates for the Schr\"{o}dinger equation on waveguide manifolds, and use them to establish upper bounds on the growth of Sobolev norms for the nonlinear Schr\"{o}dinger equation on three-dimensional waveguides.