Abstract:
Equivariant wave maps from into have smooth, stationary solutions which are critical points of the energy subject to constant charge. These solutions are globally stable under equivariant perturbations. Consequently, there exists a large set of initial data, with no degree or energy restrictions, for which the Cauchy problem is globally well-posed.
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Shatah, J., Tahvildar-Zadeh, A. On the Stability of Stationary Wave Maps} . Comm Math Phys 185, 231–256 (1997). https://doi.org/10.1007/s002200050089
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DOI: https://doi.org/10.1007/s002200050089