Global well-posedness for the Maxwell-Klein-Gordon equation in \(4+1\) dimensions: small energy

DOI10.1215/00127094-2885982zbMath1329.35209arXiv1211.3527OpenAlexW2950572329MaRDI QIDQ2347581

Joachim Krieger, Jacob Sterbenz, Daniel Tataru

Publication date: 5 June 2015

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.3527

zbMATH Keywords

energy criticalMaxwell-Klein Gordon

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Maxwell equations (35Q61) Second-order semilinear hyperbolic equations (35L71)

Related Items (12)

Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation ⋮ Local well-posedness for low regularity data for the higher dimensional Maxwell-Klein-Gordon system in Lorenz gauge ⋮ Concentration compactness for the critical Maxwell-Klein-Gordon equation ⋮ Local well-posedness of the \((4 + 1)\)-dimensional Maxwell-Klein-Gordon equation at energy regularity ⋮ The hyperbolic Yang-Mills equation in the caloric gauge: local well-posedness and control of energy-dispersed solutions ⋮ On the global behavior of solutions of the Maxwell-Klein-Gordon equations ⋮ Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model ⋮ Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation ⋮ Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data ⋮ The threshold theorem for the $(4+1)$-dimensional Yang–Mills equation: An overview of the proof ⋮ The threshold conjecture for the energy critical hyperbolic Yang-Mills equation ⋮ Global well-posedness for the massive Maxwell-Klein-Gordon equation with small critical Sobolev data

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