论文标题
Lorenz Gauge中非亚伯式Chern-Simons-Higgs系统的几乎关键的规律性
Almost critical regularity of non-abelian Chern-Simons-Higgs system in the Lorenz gauge
论文作者
论文摘要
在本文中，我们考虑了在自dual相对论的非 - 亚伯里亚人Chern-simons-higgs模型上的库奇问题，该模型是$ \ mathfrak {su} {su}（n）\，（n \ ge 2）$ 2）$值field Matter Matter field $ ϕ $和Gauge Field $ a $ a $的方程式系统。根据频率定位以及无效结构，我们显示了Sobolev空间中的本地供应良好，$ h^{s+\ frac12} \ times h^s $ for $ s> \ frac14 $。我们还证明，解决方案流映射$（ϕ（0），a（0））\ mapsto（ϕ（t），a（t））$在$ h^s \ times h^σ$的起源上不可能为$ c^2 $。这意味着规律性$ h^s $，$ s> \ frac14 $几乎至关重要。
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 $\mathfrak{su}(n)\, (n \ge 2)$-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 $H^{s+\frac12} \times H^s$ for $s>\frac14$. We also prove that the solution flow map $(ϕ(0), A(0)) \mapsto (ϕ(t), A(t))$ fails to be $C^2$ at the origin of $H^s \times H^σ$ when $σ< \frac14$ regardless of $s \in \mathbb R$. This means the regularity $H^s$, $s>\frac14$ is almost critical.
