Maxwell–Dirac Equations in Four-Dimensional Minkowski Space

DOI10.1081/PDE-200044472zbMath1082.35155MaRDI QIDQ4678916

Maria Psarelli

Publication date: 23 May 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

decay estimatessmall initial dataLie derivativenull decompositiongauge invariant energy estimatesLorentz vector fieldsmassive Maxwell-Dirac equationsspacelike hyperboloids

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Second-order nonlinear hyperbolic equations (35L70) PDEs in connection with quantum mechanics (35Q40) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Hyperbolic equations on manifolds (58J45)

Related Items (10)

Small data global existence and decay for relativistic Chern-Simons equations ⋮ On multiplicity of semi-classical solutions to a nonlinear Maxwell-Dirac system ⋮ Cauchy problem for the Fermion field equation coupled with the Chern-Simons gauge ⋮ Global solvability of massless Dirac-Maxwell systems ⋮ On semi-classical limits of ground states of a nonlinear Maxwell-Dirac system ⋮ Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data ⋮ Existence and concentration of semi-classical solutions for a nonlinear Maxwell-Dirac system ⋮ A numerical method with particle conservation for the Maxwell-Dirac system ⋮ Ill-posedness of the Maxwell-Dirac system below charge in space dimension three and lower ⋮ The Crank-Nicolson Galerkin method and convergence for the time-dependent Maxwell-Dirac system under the Lorentz gauge

Cites Work

• The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties
• Asymptotic behavior of the solutions of maxwell—klein—gordon field equations in 4—dimensional minkowski space
• Unnamed Item

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