Almost critical regularity of non-abelian Chern-Simons-Higgs system in the Lorenz gauge

2020/02/11 by Cho, Yongguen, Hong, Seokchang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.04154

Abstract

In this paper we consider a Cauchy problem on the self-dual relativistic non-abelian Chern-Simons-Higgs model, which is the system of equations of \mathfraksu(n) (n ≥ 2)-valued matter field ϕ and gauge field A. Based on the frequency localization as well as the null structure we show the local well-posedness in Sobolev space H^s+\frac12 × H^s for s>\frac14. We also prove that the solution flow map (ϕ(0), A(0)) ↦ (ϕ(t), A(t)) fails to be C² at the origin of H^s × H^σ when σ< \frac14 regardless of s ∈ \mathbb R. This means the regularity H^s, s>\frac14 is almost critical.

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