Geometric evolution equations in critical dimensions

DOI10.1007/s00526-007-0100-2zbMath1127.58003OpenAlexW2078900220WikidataQ115387724 ScholiaQ115387724MaRDI QIDQ2385153

Jalal Shatah, Joseph F. Grotowski

Publication date: 11 October 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-007-0100-2

zbMATH Keywords

blow-upYang-Mills heat flowequivariant solutionsharmonic map heat flow

Mathematics Subject Classification ID

Harmonic maps, etc. (58E20) Equations in function spaces; evolution equations (58D25)

Related Items (10)

Instantons and singularities in the Yang-Mills flow ⋮ Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem ⋮ Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map ⋮ Nonlinear stability of homothetically shrinking Yang-Mills solitons in the equivariant case ⋮ Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on \(\mathbb R^2\) ⋮ On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model ⋮ Blow up dynamics for equivariant critical Schrödinger maps ⋮ Lévy Laplacian on manifold and Yang-Mills heat flow ⋮ Renormalization and blow up for the critical Yang-Mills problem ⋮ The Yang-Mills heat equation with finite action in three dimensions

Cites Work

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• A Report on Harmonic Maps
• Formal Asymptotics of Bubbling in the Harmonic Map Heat Flow
• Harmonic Mappings of Riemannian Manifolds
• Finite time blow-up for the Yang-Mills heat flow in higher dimensions

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