Mathematics – Analysis of PDEs
Scientific paper
2011-11-18
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.
Masmoudi Nader
Planchon Fabrice
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