1012.4048 (Paul Smith)

Conditional global regularity of Schroedinger maps: sub-threshold
dispersed energy    [PDF]

Paul Smith

We consider the Schroedinger map initial value problem into the sphere in 2+1 dimensions with smooth, decaying, subthreshold initial data. Assuming an a priori $L^4$ boundedness condition on the solution, we prove that the Schroedinger map system admits a unique global smooth solution provided that the initial data is sufficiently energy-dispersed. Also shown are global-in-time bounds on certain Sobolev norms of the solution. Toward these ends we establish improved local smoothing and bilinear Strichartz estimates, adapting the Planchon-Vega approach to such estimates to the nonlinear setting of Schroedinger maps.

View original: http://arxiv.org/abs/1012.4048