On the well-posedness of Maxwell-Chern-Simons-Higgs system in the Lorenz gauge
Jianjun Yuan
Discrete & Continuous Dynamical Systems - A 2014, 34(5): 2389-2403 doi: 10.3934/dcds.2014.34.2389
In this paper, we investigate the well-posedness of the Maxwell-Chern-Simons-Higgs system in the Lorenz gauge. In particular, we prove that the system is globally wellposed in the energy space. As an application, we prove that the solution of the Maxwell-Chern-Simons-Higgs system converges to that of Maxwell-Higgs system in $H^s\times H^{s-1}$($s\geq1$) as the Chern-Simons coupling constant $\kappa\rightarrow0$.
keywords: Lorenz gauge. Maxwell-Higgs Maxwell-Chern-Simons-Higgs

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