Abstract
We construct global weak solutions of the wave map problem in the class of maps with bounded energy, with values in an arbitrary compact homogeneous space, for arbitrary initial data inH 1c . The proof proceeds by a ‘penalty approximation’ method, which generalizes J.Shatah's [5] argument for the case of maps with values in then-sphere.
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Supported in part by a grant from the National Science Foundation and Science Alliance.
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Freire, A. Global weak solutions of the wave map system to compact homogeneous spaces. Manuscripta Math 91, 525–533 (1996). https://doi.org/10.1007/BF02567971
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DOI: https://doi.org/10.1007/BF02567971