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In this paper, we consider the non-abelian Chern-Simons-Higgs system in the Lorenz gauge. By exploiting the null structure of the system and using the Xs,b type spaces, we give a local well-posedness result of it.

In this paper, as in the work of Luk and Strain [“Strichartz estimates and moment bounds for the Vlasov-Maxwell system I. The 2-D and 212-D cases,” preprint arXiv:1406.0168], by using the moment estimate and inhomogeneous Strichartz estimates, we prove the global existence of the solution of the relativistic Vlasov-Maxwell-Chern-Simons system, which admits noncompact momentum support initial data.

In this paper, we show that for a class of Higgs potentials V, the 2+1-dimensional Chern-Simons-Higgs system with negative energy or zero energy together with (ddt∫|ϕ(t,x)|2dx)(0)>0 blows up in finite time.

In this paper, we investigate the local well-posedness of the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge. By exploiting the null structure in the nonlinear terms of the equations, we reprove the low regularity result by Bournaveas ["Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge," Electron. J. Differ. Equ. 2009(114), pp. 1-10]. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3645365]