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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2017
- DOI:
- 10.48550/arXiv.1702.00751
- arXiv:
- arXiv:1702.00751
- Bibcode:
- 2017arXiv170200751A
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- 35Q40;
- 35Q35 (Primary);
- 76Y05;
- 82D10
- E-Print:
- 27 pages, accepted Comm. Math. Sci