标题： 接近空间无穷远的麦克斯韦-标量场系统 显示英文标题

标题： The Maxwell-scalar field system near spatial infinity

摘要： 我们利用Friedrich关于空间无穷远的表示来研究麦克斯韦-标量场系统在空间无穷远处的渐近展开。 此分析的主要目标是理解该系统非线性对解在类空无穷远处正则性及双次齐次展开的影响，特别是当类空无穷远与类光无穷远接触的临界集处的影响。 我们分析的主要结果是，非线性相互作用使得两个场在共形边界处比场不相互作用时更加奇异。 特别是，我们在渐近展开中发现了一类全新的对数项，这些项依赖于麦克斯韦场和标量场之间的耦合常数。 我们分析了这些结果对类光无穷远处场的剥落（或更准确地说，缺乏剥落）的影响。 显示英文摘要

摘要： We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of the non-linearities of this system on the regularity of solutions and polyhomogeneous expansions at null infinity and, in particular, at the critical sets where null infinity touches spatial infinity. The main outcome from our analysis is that the nonlinear interaction makes both fields more singular at the conformal boundary than what is seen when the fields are non-interacting. In particular, we find a whole new class of logarithmic terms in the asymptotic expansions which depend on the coupling constant between the Maxwell and scalar fields. We analyse the implications of these results on the peeling (or rather lack thereof) of the fields at null infinity.