A Sharpened Strichartz Inequality For Radial Functions

TL;DR

This paper presents a refined Strichartz inequality for radial Schrödinger solutions in two dimensions, providing a tighter bound that quantifies how close initial data are to Gaussian extremizers.

Contribution

It introduces a sharpened inequality with a negative correction term that measures the deviation from Gaussian extremizers for radial solutions.

Findings

Established an improved upper bound for radial Schrödinger solutions.

Quantified the distance from initial data to Gaussian extremizers.

Provided a negative second term indicating the deviation from extremizers.

Abstract

We prove a sharpened version of the Strichartz inequality for radial solutions of the Schr\"odinger equation in $\mathbb{R}^2\times \mathbb{R}$. We establish an improved upper bound for functions that nearly extremize the inequality, with a negative second term that measures the distance from the initial data to Gaussians.