Analysis reveals global existence and uniqueness of classical solutions for Maxwell-Chern-Simons-Higgs systems, suggesting well-posedness in (2+1) dimensions.
In this paper, we show the global existence and uniqueness of classical solutions of the Maxwell-Chern-Simmons-Higgs system coupled to a neutral scalar with nontrivial scalar potential on (2+1) dimensional Minkowski spacetime. Our methods rely only on classical existence theorems, including energy estimates, the Sobolev inequality, and the choice of the Coulomb gauge condition. The equations are well-posed for finite initial data and the solution preserves any additional H s regularity for s > 0 in the data.
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Mulyanto et al. (2025) studied this question.
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