Nonlinear Maxwell-Schroedinger system and Quantum Magneto-Hydrodynamics in 3D

TL;DR

This paper investigates the Maxwell-Schroedinger system with nonlinearities in three dimensions, establishing local and global solutions, and applying these results to quantum magnetohydrodynamics models.

Contribution

It provides the first well-posedness and global existence results for the nonlinear Maxwell-Schroedinger system in 3D, and links these to quantum magnetohydrodynamics.

Findings

Established local well-posedness in H^2 x H^{3/2} spaces.

Proved global existence of finite energy weak solutions.

Applied results to quantum magnetohydrodynamic systems.

Abstract

Motivated by some models arising in quantum plasma dynamics, in this paper we study the Maxwell-Schr\"odinger system with a power-type nonlinearity. We show the local well-posedness in $H^2(\mathbb{R}^3)\times H^{3/2}(\mathbb{R}^3)$ and the global existence of finite energy weak solutions, these results are then applied to the analysis of finite energy weak solutions for Quantum Magnetohydrodynamic systems.