On the Cauchy problem for the magnetic Zakharov system

TL;DR

This paper establishes local existence and uniqueness results for the magnetic Zakharov system, which models plasma-wave interactions involving magnetic fields, using energy methods and approximation techniques.

Contribution

It provides the first rigorous proof of local well-posedness for the magnetic Zakharov system in two and three dimensions.

Findings

Proved local existence of solutions in 2D and 3D.

Established uniqueness of solutions.

Developed a priori bounds using energy methods.

Abstract

In this paper, we study the Cauchy problem of the magnetic type Zakharov system which describes the pondermotive force and magnetic field generation effects resulting from the non-linear interaction between plasma-wave and particles. By using the energy method to derive a priori bounds and an approximation argument for the construction of solutions, we obtain local existence and uniqueness results for the magnetic Zakharov system in the case of $d=2,3$.