Abstract
In the present paper we prove the global unique solvability of the Cauchy problem for the Yang-Mills-Higgs equations in a Hamiltonian calibration in the four-dimensional Minkowski space-time for any behavior of the initial data at spatial infinity. In particular, the configuration of the initial data, and therefore, also the solution for all t, may have an arbitrary magnetic charge. In addition, also a spontaneous break of symmetry is admitted.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 18–48, 1985.
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Goganov, M.V., Kapitanskii, L.V. Global solvability of the Cauchy problem for the Yang-Mills-HIGGS equations. J Math Sci 37, 802–822 (1987). https://doi.org/10.1007/BF01387720
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DOI: https://doi.org/10.1007/BF01387720