Generalized Strichartz estimates and scattering for 3D Zakharov system

TL;DR

This paper proves scattering for the 3D Zakharov system with small non-radial data by establishing a generalized Strichartz estimate that incorporates angular regularity, advancing understanding of dispersive PDEs.

Contribution

It introduces a generalized Strichartz estimate for the Schrödinger equation with angular regularity, enabling scattering results for the 3D Zakharov system with non-radial data.

Findings

Scattering established for small non-radial data in the energy space.

Generalized Strichartz estimate proven for Schrödinger equation with angular regularity.

Method extends previous radial symmetry results to non-radial cases.

Abstract

We obtain scattering for the 3D Zakharov system with non-radial small data in the energy space with angular regularity of degree one. The main ingredient is a generalized Strichartz estimate for the Schr\"odinger equation in the space of $L^2$ angular integrability.