Global regularity of critical Schrödinger maps: subthreshold dispersed energy

Abstract

We consider the energy-critical Schroedinger map initial value problem with smooth initial data from R^2 into the sphere S^2. Given sufficiently energy-dispersed data with subthreshold energy, we prove that the system admits a unique global smooth solution. This improves earlier analogous conditional results. The key behind this improvement lies in exploiting estimates on the commutator of the Schroedinger map and harmonic map heat flows.

28 pages; streamlined exposition; some material originally appearing in earlier versions of this manuscript has instead been incorporated into 1012:4048

References in corpus (5)

• Regularity of Wave-Maps in dimension 2+1
• Energy dispersed large data wave maps in 2+1 dimensions
• On Schrödinger Maps
• Geometric renormalization below the ground state
• Global results for Schrödinger Maps in dimensions $n\ge 3$

Cited by in corpus (4)

• Finite energy global well-posedness of the Yang-Mills equations on ${\mathbb{R}}^{1+3}$: An approach using the Yang-Mills heat flow
• Gauge choice for the Yang-Mills equations using the Yang-Mills heat flow and local well-posedness in $H^1$
• On the cubic NLS on 3D compact domains
• Bilinear Strichartz estimates for the Schr{ö}dinger map problem