Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

TL;DR

This paper establishes local well-posedness for the 2D Klein-Gordon-Zakharov system with low regularity initial data using bilinear estimates and Fourier analysis techniques.

Contribution

It introduces new bilinear estimates and applies advanced Fourier restriction methods to prove well-posedness for low regularity initial data in the 2D Klein-Gordon-Zakharov system.

Findings

Bilinear estimates crucial for well-posedness

Application of Fourier restriction norm method

Use of nonlinear Loomis-Whitney inequality

Abstract

This paper is concerned with the Cauchy problem of $2$D Klein-Gordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get the local in time well-posedness. The estimates are established by the Fourier restriction norm method. We utilize the bilinear Strichartz estimates and the nonlinear version of the classical Loomis-Whitney inequality which was applied to Zakharov system.