Communications in Mathematical Sciences

Volume 15 (2017)

Number 2

Nonlinear Maxwell–Schrödinger system and quantum magneto-hydrodynamics in $\textsf{3-D}$

Pages: 451 – 479

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n2.a7

Authors

Paolo Antonelli (Gran Sasso Science Institute, L’Aquila, Italy)

Michele d’Amico (Gran Sasso Science Institute, L’Aquila, Italy)

Pierangelo Marcati (Gran Sasso Science Institute, L’Aquila, Italy; and Dept. of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Italy)

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.

Keywords

nonlinear Maxwell–Schrödinger, nuantum magnetohydrodynamics, finite energy solutions

2010 Mathematics Subject Classification

Primary 35Q35, 35Q40, 35Q55. Secondary 76Y05, 82D10.

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Published 21 February 2017