Spherical Averaged Endpoint Strichartz Estimates for The Two-dimensional Schrodinger Equations with Inverse Square Potential

TL;DR

This paper proves endpoint Strichartz estimates for 2D Schrödinger equations with inverse square potential, showing they hold for radial data and are recovered via angular averaging, extending previous results.

Contribution

It establishes the validity of endpoint estimates for Schrödinger equations with inverse square potential using angular averaging techniques, including for radial data.

Findings

Endpoint estimates hold for inverse square potential cases.

Radial data satisfies the endpoint estimates.

Averaging in angular variables recovers classical estimates.

Abstract

The endpoint Strichartz estimates for two-dimensional Schrodinger equations were recovered by averaging the solutions in L^2 in the angular variable by Tao. For Schrodinger equations with defocusing inverse square potential, we proved that the homogeneous endpoint estimates hold under this setting. In particular, the original versions of endpoint estimates hold for radial data.