Global solutions of two coupled Maxwell systems in the temporal gauge

Jianjun  Yuan

doi:10.3934/dcds.2016.36.1709

Article Contents

2016, Volume 36, Issue 3: 1709-1719. Doi: 10.3934/dcds.2016.36.1709

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Global solutions of two coupled Maxwell systems in the temporal gauge

Jianjun Yuan^1,

1.
The College of Information and Technology, Nanjing University of Chinese Medicine, Nanjing 210046

Received: November 30, 2014

Revised: February 28, 2015

Published: May 2017

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Abstract

In this paper, we consider the Maxwell-Klein-Gordon and Maxwell-Chern-Simons-Higgs systems in the temporal gauge. By using the fact that when the spatial gauge potentials are in the Coulomb gauge, their $\dot{H}^1$ norms can be controlled by the energy of the corresponding system and their $L^2$ norms, and the gauge invariance of the systems, we show that finite energy solutions of these two systems exist globally in this gauge.

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Mathematics Subject Classification: 35Q61, 35A01, 35B30.

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References

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