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arXiv · 1310.3955

Finite energy global well-posedness of the Chern-Simons-Higgs equations in the Coulomb gauge

Sung-Jin Oh
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Abstract

In a recent paper, Selberg-Tesfahun proved that the abelian Chern-Simons-Higgs system (CSH) is globally well-posed for finite energy initial data under the Lorenz gauge condition. It has been suspected by Huh, however, that such a result should hold in the Coulomb gauge as well. In this note, we give an affirmative answer to this question by first establishing low regularity local well-posededness of (CSH) in the Coulomb gauge for initial data set $(f, g) \in H^γ_{x} \times H^{γ-1}_{x}$ for any $γ> 3/4$. Then by conservation of energy, global well-posedness for (CSH) in the energy space $(f, g) \in H^{1}_{x} \times L^{2}_{x}$ follows rather immediately.

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Sung-Jin Oh. 2013-10-15. Finite energy global well-posedness of the Chern-Simons-Higgs equations in the Coulomb gauge. https://arxiv.org/abs/1310.3955

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