Fast and Slow Blowup in the S^2 Sigma Model and (4+1)-Dimensional Yang-Mills Model

Abstract

We study singularity formation in spherically symmetric solutions of the charge-one and charge-two sector of the (2+1)-dimensional S^2 sigma-model and the (4+1)-dimensional Yang-Mills model, near the adiabatic limit. These equations are non-integrable, and so studies are performed numerically on rotationally symmetric solutions using an iterative finite differencing scheme that is numerically stable. We evaluate the accuracy of predictions made with the geodesic approximation. We find that the geodesic approximation is extremely accurate for the charge-two sigma-model and the Yang-Mills model, both of which exhibit fast blowup. The charge-one sigma-model exhibits slow blowup. There the geodesic approximation must be modified by applying an infrared cutoff that depends on initial conditions.

30 pages including 11 embedded figures and 2 tables. Some of these results were previously reported in math-ph/9909015 and math-ph/9909014

References in corpus (2)

• Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere
• Numerical investigations of singularity formation in non-linear wave equations in the adiabatic limit

Cited by in corpus (9)

• Motion on moduli spaces with potentials
• Collapse of an Instanton
• On collapse of wave maps
• Slow equivariant lump dynamics on the two sphere
• The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps
• A globally stable self-similar blowup profile in energy supercritical Yang-Mills theory
• Quantum lump dynamics on the two-sphere
• Stable self-similar blowup in energy supercritical Yang-Mills theory
• The adiabatic limit of wave map flow on a two torus