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

Abstract

Motivated by some models arising in quantum plasma dynamics, in this paper we study the Maxwell-Schrödinger 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.

27 pages, accepted Comm. Math. Sci