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Towards the Chern-Simons-Higgs equation with finite energy

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

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