Well-posedness for an hyperbolic-hyperbolic-elliptic system describing cold plasmas

TL;DR

This paper establishes the well-posedness of a complex PDE system modeling collision-free plasma dynamics in magnetic fields, using a combination of pointwise estimates and bootstrap arguments.

Contribution

It provides the first rigorous proof of well-posedness for this specific hyperbolic-hyperbolic-elliptic plasma system, combining novel analytical techniques.

Findings

Proved well-posedness of the PDE system

Developed a new analytical approach for the elliptic component

Validated the mathematical model for plasma motion

Abstract

In this short note, we provide the well-posedness for an hyperbolic-hyperbolic-elliptic system of PDEs describing the motion of collision free-plasma in magnetic fields. The proof combines a pointwise estimate together with a bootstrap type of argument for the elliptic part of the system.