论文标题
关于弱的零状况的富麦
A Fuchsian viewpoint on the weak null condition
论文作者
论文摘要
我们分析了$ 3+1 $尺寸的半线性波方程的系统，其相关的渐近方程允许有限的解决方案，以适当地选择初始数据。在这种弱零条件的特殊情况下，我们称之为\ textit {有限的弱空条件}，我们证明了在较小的初始数据假设下，在空间无穷大的邻域中，这些波动方程的解决方案存在。使用Fuchsian方法建立了存在。该方法涉及将波程方程转换为在有界时空区域定义的紫色方程。然后，Fuchsian方程的解决方案的存在源于\ cite {boos：2020}中的存在理论的应用。反过来，这是通过构造的解决方案来产生的，该解决方案是空间无穷大街区的波动方程式原始系统。
We analyze systems of semilinear wave equations in $3+1$ dimensions whose associated asymptotic equation admit bounded solutions for suitably small choices of initial data. Under this special case of the weak null condition, which we refer to as the \textit{bounded weak null condition}, we prove the existence of solutions to these systems of wave equations on neighborhoods of spatial infinity under a small initial data assumption. Existence is established using the Fuchsian method. This method involves transforming the wave equations into a Fuchsian equation defined on a bounded spacetime region. The existence of solutions to the Fuchsian equation then follows from an application of the existence theory developed in \cite{BOOS:2020}. This, in turn, yields, by construction, solutions to the original system of wave equations on a neighborhood of spatial infinity.
