The Cauchy problem for the coupled Maxwell–Schrödinger equations

DOI10.1063/1.527363zbMath0606.35015OpenAlexW2022540599MaRDI QIDQ3744545

Kuniaki Nakamitsu, Masayoshi Tsutsumi

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1063/1.527363

zbMATH Keywords

existenceuniquenesselectro-magnetic fieldCauchy initial value problemnonrelativistic charged particleMaxwell-Schrödinger equationscomplex scalar fieldLorentz gauge conditionquantum field equations

Mathematics Subject Classification ID

Initial value problems for nonlinear higher-order PDEs (35G25) Partial differential equations of mathematical physics and other areas of application (35Q99) Motion of charged particles (78A35)

Related Items

Global solution in a weak energy class for Klein-Gordon-Schrödinger system, Global well-posedness for the non-linear Maxwell-Schrödinger system, Global finite-energy solutions of the Maxwell-Schrödinger system, Energy solution to the Chern-Simons-Schrödinger equations, 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, Time global finite-energy weak solutions to the many-body Maxwell-Pauli equations, A Crank--Nicolson Finite Element Method and the Optimal Error Estimates for the Modified Time-Dependent Maxwell--Schrödinger Equations, Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell-Schrödinger equations, Solitons in Schrödinger-Maxwell equations, Long range scattering for the Maxwell-Schrödinger system with large magnetic field data and small Schrödinger data, Global existence and uniqueness of solutions to the Maxwell-Schrödinger equations, Local well-posedness for the Maxwell-Schrödinger equation, Global existence and asymptotic behavior of solutions for the Maxwell- Schrödinger equations in three space dimensions

Cites Work

• The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge
• Remarks on the Korteweg-de Vries equation
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• On semi-linear parabolic partial differential equations