标题： 黑洞上的麦克斯韦-希格斯系统的衰减估计 显示英文标题

标题： Decay Estimate of Maxwell-Higgs System on Schwarzschild Black Holes

摘要： 在本文中，我们证明了四维施瓦茨希尔德时空上的麦克斯韦-希格斯系统的衰减估计。 我们表明，如果场方程在被困表面上支持一种莫拉韦茨类型的估计，则可以通过使用索博列夫不等式和能量估计获得施瓦茨希尔德黑洞整个外部区域的均匀衰减性质。 我们的结果还考虑了各种形式的物理势能，如质量项、$\phi^4$理论、正弦-戈登势能和托达势能。 显示英文摘要

摘要： In this paper, we prove the decay estimate of Maxwell-Higgs system on four dimensional Schwarzschild spacetimes. We show that if the field equations support a Morawetz type estimate supported around the trapped surface, the uniform decay properties in the entire exterior of the Schwarzschild black holes can be obtained by using Sobolev inequalities and energy estimates. Our results also consider various forms of physical potential such as the mass terms, $\phi^4$-theory, sine Gordon potential, and Toda potential.