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

2017/02/02 by Antonelli, Paolo, D'Amico, Michele, Marcati, Pierangelo
#35Q35 (Primary) #35Q40 #76Y05 #82D10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1702.00751

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 H²(ℝ³)× H^3/2(ℝ³) 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.

Related

• Existence and Stability of almost finite energy weak solutions to the Quantum Euler-Maxwell system
• Global wellposedness in the energy space for the Maxwell-Schrödinger system
• Global existence of weak solutions for quantum MHD equations
• Quantum Magnetohydrodynamics
• Genuine Hydrodynamic Analysis to the 1-D QHD system: Existence, Dispersion and Stability