Towards the Chern-Simons-Higgs equation with finite energy

Hyungjin Huh

doi:10.3934/dcds.2011.30.1145

Article Contents

2011, Volume 30, Issue 4: 1145-1159. Doi: 10.3934/dcds.2011.30.1145

This issue Previous Article A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative Ricci curvature Next Article Some remarks for a modified periodic Camassa-Holm system

Towards the Chern-Simons-Higgs equation with finite energy

Hyungjin Huh^1,

1.
Department of Mathematics, Chung-Ang University, Seoul 156-756

Received: September 30, 2009

Revised: December 31, 2010

Published: September 2011

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Abstract

Under the Coulomb gauge condition Chern-Simons-Higgs equations are formulated in the hyperbolic system coupled with elliptic equations. We consider a solution of Chern-Simons-Higgs equations with finite energy and show how to obtain $H^1$ solution with one exceptional term $\phi\partial_t A_0$ from which the model equations (63) are proposed.

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Mathematics Subject Classification: Primary: 35L15, 35L45; Secondary: 35Q40.

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