Regularity of Wave-Maps in dimension 2+1

In this article we prove a Sacks-Uhlenbeck/Struwe type global regularity result for wave-maps $\Phi:\mathbb{R}^{2+1}\to\mathcal{M}$ into general compact target manifolds $\mathcal{M}$.Comment: 31 page

Local energy decay for Maxwell fields part I: Spherically symmetric black-hole backgrounds

We prove local energy decay estimates for solutions to the inhomogeneous Maxwell system on a generic class of spherically symmetric black holes.Comment: v2. Added some references. Improved exposition and one new diagram. Journal versio