# American Institute of Mathematical Sciences

May  2014, 34(5): 2389-2403. doi: 10.3934/dcds.2014.34.2389

## On the well-posedness of Maxwell-Chern-Simons-Higgs system in the Lorenz gauge

 1 Department of Basic Science, Yancheng Institute of Technology, Yancheng 224051, China

Received  March 2013 Revised  July 2013 Published  October 2013

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 $\kappa\rightarrow0$.
Citation: Jianjun Yuan. On the well-posedness of Maxwell-Chern-Simons-Higgs system in the Lorenz gauge. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2389-2403. doi: 10.3934/dcds.2014.34.2389
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