Unconditional well-posedness for wave maps

Details Unconditional well-posedness for wave maps Unconditional well-posedness for wave maps

2011-11-18

arxiv.org/abs/1111.4374v1

Mathematics

Analysis of PDEs

16 pages, to appear in J. Hyperbolic Differ. Equ

Scientific paper

We prove uniqueness of solutions to the wave map equation in the natural class, namely $ (u, \partial_t u) \in C([0,T); \dot{H}^{d/2})\times C^1([0,T); \dot{H}^{d/2-1})$ in dimensions $d\geq 4$. This is achieved through estimating the difference of two solutions at a lower regularity level. In order to reduce to the Coulomb gauge, one has to localize the gauge change in suitable cones as well as estimate the difference between the frames and connections associated to each solutions and take advantage of the assumption that the target manifold has bounded curvature.

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