Jinhua Wang: Long time solutions for wave maps with large data.

For 2 + 1 dimensional wave maps with \(\mathbb{S}^{2}\) as the target, we show that for all positive numbers \(T_{0}>0\) and \(E_{0}>0\), there exist Cauchy initial data with energy at least \(E_{0}\), so that the solution’s life-span is at least \([0,T_{0}]\). We assume neither symmetry nor closeness to harmonic maps.