The Global Existence and Uniqueness of Maxwell-Chern-Simons-Higgs Equation in (2+1) Dimensions

TL;DR

This paper proves the global existence and uniqueness of classical solutions for the Maxwell-Chern-Simons-Higgs system in (2+1) dimensions, using classical methods like energy estimates and gauge conditions.

Contribution

It establishes the well-posedness of the Maxwell-Chern-Simons-Higgs equations with scalar potential on (2+1)D Minkowski space, a result not previously shown.

Findings

Solutions exist globally and are unique for finite initial data.

Solutions preserve higher regularity if present in initial data.

The methods rely on classical energy estimates and gauge choices.

Abstract

In this paper, we show the global existence and uniqueness of classical solutions of the Maxwell-Chern-Simmons-Higgs system coupled to a neutral scalar with nontrivial scalar potential on (2+1) dimensional Minkowski spacetime. Our methods rely only on classical existence theorems, including energy estimates, the Sobolev inequality, and the choice of the Coulomb gauge condition. The equations are well-posed for finite initial data and the solution preserves any additional $H^{s}$ regularity for $s>0$ in the data.