Scattering for the Zakharov system in 3 dimensions

TL;DR

This paper proves global existence and scattering for small localized solutions of the 3D Zakharov system, demonstrating optimal decay rates for wave and Schrödinger components.

Contribution

It establishes the first rigorous proof of global scattering and decay rates for the 3D Zakharov system with small initial data.

Findings

Wave component decays at t^{-1}

Schrödinger component decays at t^{-7/6}

Global existence for small localized solutions

Abstract

We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t^{-1}, whereas the Schr\"odinger component decays almost at a rate of t^{-7/6}.