Local existence for the maxwell-dirac equations in three space dimensions

DOI10.1080/03605309608821204zbMath0880.35116OpenAlexW1995856402MaRDI QIDQ4887929

Nikolaos Bournaveas

Publication date: 28 January 1998

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

Full work available at URL: https://doi.org/10.1080/03605309608821204

zbMATH Keywords

existenceuniquenesslocal solutionMaxwell-Dirac equations

Mathematics Subject Classification ID

Related Items (20)

Global Regularity for General Non-Linear Wave Equations I. (6 + 1) and Higher Dimensions ⋮ Local existence of energy class solutions for the dirac—klein—gordon equations ⋮ An efficient and stable numerical method for the Maxwell--Dirac system ⋮ A spherically symmetric bound state of the coupled Maxwell-Dirac equations with self-interaction alone ⋮ Local well-posedness for the Maxwell-Dirac system in temporal gauge ⋮ BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS ⋮ Cauchy problem for the Fermion field equation coupled with the Chern-Simons gauge ⋮ A simple and accurate mixed \(P^{0}-Q^{1}\) solver for the Maxwell-Dirac equations ⋮ The modified scattering for Dirac equations of scattering-critical nonlinearity ⋮ On global attraction to quantum stationary states. Dirac equation with mean field interaction ⋮ Global well-posedness of the Maxwell-Dirac system in two space dimensions ⋮ Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data ⋮ Global solution to Maxwell-Dirac equations in \(1+1\) dimensions ⋮ Variational methods in relativistic quantum mechanics ⋮ A numerical method with particle conservation for the Maxwell-Dirac system ⋮ Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime ⋮ ON THE ASYMPTOTIC ANALYSIS OF THE DIRAC–MAXWELL SYSTEM IN THE NONRELATIVISTIC LIMIT ⋮ On spectral stability of the nonlinear Dirac equation ⋮ Ill-posedness of the Maxwell-Dirac system below charge in space dimension three and lower ⋮ Convergence of the Dirac–Maxwell System to the Vlasov–Poisson System

Cites Work

• On the Maxwell-Klein-Gordon equation with finite energy
• Finite energy solutions of the Yang-Mills equations in \(\mathbb{R}^{3+1}\)
• A priori estimates for the wave equation and some applications
• Commutator estimates and the euler and navier-stokes equations
• Regularity for the wave equation with a critical nonlinearity
• Space‐time estimates for null forms and the local existence theorem
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