Global wellposedness in the energy space for the Maxwell-Schrödinger system

DOI10.1007/s00220-009-0765-9zbMath1171.81006arXiv0712.0098OpenAlexW1968465795MaRDI QIDQ842459

Daniel Tataru, Ioan Bejenaru

Publication date: 25 September 2009

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

Full work available at URL: https://arxiv.org/abs/0712.0098

Mathematics Subject Classification ID

Bootstrap, jackknife and other resampling methods (62F40) PDEs in connection with optics and electromagnetic theory (35Q60) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Electromagnetic interaction; quantum electrodynamics (81V10) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (13)

Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field ⋮ Global well-posedness for the non-linear Maxwell-Schrödinger system ⋮ Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation ⋮ Long range scattering for the Maxwell-Schrödinger system in the Lorenz gauge without any restriction on the size of data ⋮ Large data well-posedness in the energy space of the Chern-Simons-Schrödinger system ⋮ Time global finite-energy weak solutions to the many-body Maxwell-Pauli equations ⋮ Existence and uniqueness of local regular solution to the Schrödinger flow from a bounded domain in \(\mathbb{R}^3\) into \(\mathbb{S}^2\) ⋮ Klein-Gordon-Schrödinger system: Dinucleon field ⋮ Equivariant heat and Schrödinger flows from Euclidean space to complex projective space ⋮ Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces ⋮ Local nonautonomous Schrödinger flows on Kähler manifolds ⋮ A refined stability result for standing waves of the Schrödinger–Maxwell system ⋮ On quantum jumps and attractors of the Maxwell-Schrödinger equations

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• Endpoint Strichartz estimates
• Dispersive estimates for principally normal pseudodifferential operators
• A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
• Wave packet parametrices for evolutions governed by pdo's with rough symbols

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