Nonlinear Maxwell-Schrödinger system and quantum magneto-hydrodynamics in 3-D

DOI10.4310/CMS.2017.v15.n2.a7zbMath1372.35280arXiv1702.00751OpenAlexW2590121331WikidataQ58619704 ScholiaQ58619704MaRDI QIDQ2627197

Pierangelo Marcati, Paolo Antonelli, Michele d'Amico

Publication date: 30 May 2017

Published in: Communications in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.00751

zbMATH Keywords

local existenceweak solutionsglobal existencegauge invariancequantum plasmas

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Weak solutions to PDEs (35D30)

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Global well-posedness for the non-linear Maxwell-Schrödinger system ⋮ Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials ⋮ Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation ⋮ Time global finite-energy weak solutions to the many-body Maxwell-Pauli equations ⋮ A refined stability result for standing waves of the Schrödinger–Maxwell system ⋮ Large-time behavior of solutions to the bipolar quantum Navier-Stokes-Poisson equations ⋮ Remarks on the derivation of finite energy weak solutions to the QHD system

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