Sharp spherically averaged Strichartz estimates for the Schr\"odinger equation

TL;DR

This paper establishes sharper spherically averaged Strichartz estimates for the Schrödinger equation with weaker angular integrability and applies these results to demonstrate scattering in the 3D Zakharov system with low angular regularity.

Contribution

It introduces generalized Strichartz estimates with weaker angular integrability and applies them to prove scattering in the 3D Zakharov system, improving previous results.

Findings

Sharp spherically averaged Strichartz estimates proven

Scattering established for 3D Zakharov system with low angular regularity

Estimates are sharp except at some endpoints

Abstract

We prove generalized Strichartz estimates with weaker angular integrability for the Schr\"odinger equation. Our estimates are sharp except some endpoints. Then we apply these new estimates to prove the scattering for the 3D Zakharov system with small data in the energy space with low angular regularity. Our results improve the results obtained recently in \cite{GLNW}.