Convolutions of singular measures and applications to the Zakharov system

TL;DR

This paper establishes uniform L^2 estimates for convolutions of singular measures on transversal submanifolds and applies these results to prove local well-posedness of the 3D Zakharov system in the subcritical regime.

Contribution

It extends previous work by providing uniform estimates for convolutions of singular measures and applies these to the analysis of the Zakharov system.

Findings

Proved uniform L^2 estimates for convolutions of singular measures.

Extended previous results using Bennett-Bez techniques.

Established local well-posedness of the 3D Zakharov system in the subcritical regime.

Abstract

Uniform L^2-estimates for the convolution of singular measures with respect to transversal submanifolds are proved in arbitrary space dimension. The results of Bennett-Bez are used to extend previous work of Bejenaru-Herr-Tataru. As an application, it is shown that the 3D Zakharov system is locally well-posed in the full subcritical regime.