We estimate the L^∞ norm of the first derivative of the solution to the Chern–Simons gauged O(3) sigma model in ${\mathbb{R}}^{1+1}$ by using local energy conservation and observing the transport equation along the characteristic line. As an application of the bound, we improve the growth rate of the H² norm of the solution from an exponential to a polynomial one. We also apply a similar idea to the Chern–Simons–Higgs model.

中文翻译：

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R1+1 中Chern-Simons 规范方程的L∞界及其应用

我们估计Chern-Simons 规范的O (3) 西格玛模型的解的一阶导数的L ^∞范数${\mathbb{电阻}}^{1+1}$通过使用局部能量守恒并观察沿特征线的输运方程。作为界限的应用，我们将解的H ²范数的增长率从指数提高到多项式。我们也将类似的想法应用于 Chern-Simons-Higgs 模型。