Local well-posedness of a system describing laser-plasma interactions

TL;DR

This paper proves local well-posedness for a degenerate Zakharov system modeling laser-plasma interactions, handling rough initial data using advanced analytical techniques.

Contribution

It introduces a new local well-posedness result for rough initial data in a degenerate Zakharov system, employing local smoothing and maximal function norms.

Findings

Established local well-posedness for rough initial data

Utilized local smoothing and maximal function norms in proof

Applicable to laser-plasma interaction models

Abstract

A degenerate Zakharov system arises as a model for the description of laser-plasma interactions. It is a coupled system of a Schr\"odinger and a wave equation with a non-dispersive direction. In this paper, a new local well-posedness result for rough initial data is established. The proof is based on an efficient use of local smoothing and maximal function norms.