AI 中文总结
本文是系列论文第二篇，独立于前篇，利用柱对称性等为三维相对论性Vlasov - Maxwell系统的局部电磁场建立两组逐点估计，对迭代平滑方案至关重要，还根据振荡相位量化平滑效应，解决无平滑效应情况构成自举论证初始挑战。
AI 中文摘要
这是两篇系列论文的第二篇，其确立了具有柱对称性的任意大光滑局部初始数据的三维相对论性Vlasov - Maxwell系统（RVM）的全局存在性。在第二部分中，独立于第一部分的结果，我们为局部电磁场建立了两组逐点估计。通过利用柱对称性、守恒定律、平滑效应以及电磁场的结构观察（包括其零结构、双零结构和磁场二分法）来实现。第一组为局部电磁场提供了一个统一的上界。第二组给出了一个依赖于到z轴距离的上界，当电磁场离z轴更远时能提供更好的控制。这两组估计对于由Klainerman - Staffilani（2002）的工作启发而来的迭代平滑方案（ISS）至关重要。在第一部分中这两组估计被视为黑箱。这些估计的一个显著特征是它们根据特征时间上振荡相位的值来评估，有效地量化了平滑效应。由此可知没有任何平滑效应的情况是误差项。解决这个问题构成了自举论证中的初始挑战。
英文摘要
This is the second part of a two-paper sequence establishing the global existence of $3D$ relativistic Vlasov-Maxwell system (RVM) for arbitrarily large smooth localized initial data with cylindrical symmetry. In Part II, independently of the results in Part I, we establish two sets of pointwise estimates for the localized electromagnetic field. This is achieved by exploiting cylindrical symmetry, conservation laws, smoothing effects, and structural observations of the electromagnetic field, including its null structure, double null structure, and the magnetic field dichotomy. The first set provides a uniform upper bound for the localized electromagnetic field. The second set offers an upper bound that depends on the distance from the z-axis, providing better control when the electromagnetic field is located further away from the $z$-axis. These two sets of estimates are fundamental to the iterative smoothing scheme (ISS), which is originated and inspired by the work of Klainerman-Staffilani(2002). These two sets were treated as black boxes in Part I. A defining feature of these estimates is that they are assessed concerning the magnitude of the oscillation phase over characteristic time, effectively quantifying the smoothing effect. It follows from these estimates that cases without any smoothing effect are error terms. Addressing this constitutes the initial challenge in the bootstrap argument.
CommentsMany thanks to the reports received during the submission process of the preprint arXiv:2203.01199, it has been reformatted and divided into two parts. This is the second part. arXiv admin note: substantial text overlap with arXiv:2203.01199
