Strichartz estimates for quasi-periodic functions and applications

TL;DR

This paper establishes Strichartz estimates for quasi-periodic functions with decaying Fourier coefficients using $\

Contribution

It introduces new Strichartz estimates for quasi-periodic functions and applies multilinear refinements to improve low regularity well-posedness results for nonlinear Schrödinger equations.

Findings

Strichartz estimates for quasi-periodic functions are proven.

Enhanced low regularity local well-posedness results for nonlinear Schrödinger equations.

Achieves sharp local well-posedness for the cubic nonlinear Schrödinger equation.

Abstract

We show Strichartz estimates for quasi-periodic functions with decaying Fourier coefficients via $\ell^2$-decoupling. When we additionally average in time, further improvements can be obtained. Next, we apply multilinear refinements to show low regularity local well-posedness for nonlinear Schr\"odinger equations. For the cubic nonlinear Schr\"odinger equation the approach yields the sharp local well-posedness result.