Strichartz estimates in Wiener amalgam spaces for Schr\"{o}dinger equations with at most quadratic potentials

TL;DR

This paper establishes Strichartz estimates in Wiener amalgam spaces for Schrödinger equations with potentials growing at most quadratically, enhancing local regularity analysis beyond classical Lebesgue space estimates.

Contribution

It generalizes previous results by proving Strichartz estimates in Wiener amalgam spaces for a broader class of quadratic potentials.

Findings

Strichartz estimates hold in Wiener amalgam spaces for quadratic potentials.

Enhanced local-in-space regularity compared to classical estimates.

Extension of prior work to more general quadratic potentials.

Abstract

For Schr\"{o}dinger equations with potentials which grow at most quadratically at spatial infinity, we prove Strichartz estimates in Wiener amalgam spaces. These estimates provide a stronger recovery of local-in-space regularity than the classical Strichartz estimates in Lebesgue spaces. Our result is a generalization of the results on Strichartz estimates in Wiener amalgam spaces by Cordero and Nicola, which are stated for the potentials $V(x) = 0,|x|^2/2, -|x|^2/2$.