Some new Strichartz estimates for the Schr\"odinger equation

TL;DR

This paper introduces new Strichartz estimates for the Schr"odinger equation on Wiener amalgam spaces, extending classical results and applying them to establish well-posedness with rough potentials.

Contribution

It provides generalized Strichartz estimates on Wiener amalgam spaces and demonstrates their use in proving well-posedness for Schr"odinger equations with irregular potentials.

Findings

New generalized Strichartz estimates for Schr"odinger propagator

Sharpness analysis of existing estimates

Well-posedness results with rough time-dependent potentials

Abstract

We deal with fixed-time and Strichartz estimates for the Schr\"odinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones. As an application, we present a result on the wellposedness of the linear Schr\"odinger equation with a rough time dependent potential.