Jacob Sterbenz

Regularity of Wave-Maps in Dimension 2 + 1

In this article we prove a Sacks-Uhlenbeck/Struwe type global regularity result for wave-maps

Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions

{\Phi:\mathbb{R}^{2+1} \to\mathcal{M} }

Global stability for charged-scalar fields on Minkowski space

into general compact target manifolds

Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzschild Space

{\mathcal{M} }

An Endpoint

.

(1,\infty)

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular momentum operators. In this setting, the range of (q,r) exponents vastly improves over what is available for the wave equations based on translation invariant derivatives of the initial data and the dispersive inequality. Two proofs of this result are given.