Global regularity for the Yang–Mills equations on high dimensional Minkowski space

DOI10.1090/S0065-9266-2012-00566-1zbMath1304.35005arXivmath/0503382OpenAlexW1995271761MaRDI QIDQ4979154

Jacob Sterbenz, Joachim Krieger

Publication date: 17 June 2014

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503382

zbMATH Keywords

critical regularityYang-Mills equationswave-equationCrönstrom gauge transformationsmicrolocal geometric renormalization

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (15)

On the stability of self-similar solutions to nonlinear wave equations ⋮ Infinite energy solutions for the \((3+1)\)-dimensional Yang-Mills equation in Lorenz gauge ⋮ Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation ⋮ Concentration compactness for the critical Maxwell-Klein-Gordon equation ⋮ A Globally Stable Self-Similar Blowup Profile in Energy Supercritical Yang-Mills Theory ⋮ The hyperbolic Yang-Mills equation in the caloric gauge: local well-posedness and control of energy-dispersed solutions ⋮ Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation ⋮ The threshold theorem for the $(4+1)$-dimensional Yang–Mills equation: An overview of the proof ⋮ Stable self-similar blowup in energy supercritical Yang-Mills theory ⋮ Low Regularity Well-Posedness for the Yang--Mills System in Fourier--Lebesgue Spaces ⋮ The threshold conjecture for the energy critical hyperbolic Yang-Mills equation ⋮ Local well-posedness for the \((n + 1)\)-dimensional Yang-Mills and Yang-Mills-Higgs system in temporal gauge ⋮ Global well-posedness for the massive Maxwell-Klein-Gordon equation with small critical Sobolev data ⋮ Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge ⋮ Global well-posedness for the Maxwell-Klein-Gordon equation in \(4+1\) dimensions: small energy

Cites Work

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• Sharp local well-posedness results for the nonlinear wave equation
• Global regularity for the Maxwell-Klein-Gordon equation with small critical Sobolev norm in high dimensions
• Connections with \(L^ p \)bounds on curvature
• Improved local well-posedness for quasilinear wave equations in dimension three
• On the well-posedness of the wave map problem in high dimensions
• Endpoint Strichartz estimates

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