具有吸引耦合的相对论Vlasov-泊松方程单位质量零能维里小于-1/2球形初值的存在性
Existence of Spherical Initial Data with Unit Mass, Zero Energy, and Virial less than - 1/2 for the Relativistic Vlasov-Poisson Equation with Attractive Coupling
摘要：
Kiessling和Tahvildar-Zadeh在最近的一篇论文中证明了具有吸引耦合的相对论性Vlasov-泊松方程的任何经典解在总能量为零且维里小于或等于-1/2的球对称初始数据下都会在有限时间内爆破。他们不知道是否存在这样的数据。随后，有人提出是否存在任何此类数据的问题。事实上，最简单的可想象的无穷大，一个以原点为中心的几乎均匀的物质球，动量指向内部，维里必须严格大于-1/2！在这篇简短的笔记中，我们通过构造两类这样的初始数据来解决这个问题。
英文摘要：
In a recent paper, Kiessling and Tahvildar-Zadeh proved that any classical solution of the relativistic Vlasov-Poisson equation with attractive coupling launched by spherically symmetric initial data with zero total energy and virial less than or equal to -1/2 will blow up in finite time. They left open whether such data exist. Subsequently, the question was raised whether any such data exist at all. In fact, the simplest conceivable ansatz, a nearly uniform ball of material centered at the origin with momenta directed inward, must have virial strictly larger than -1/2! In this brief note, we settle this issue by constructing two classes of such initial data.
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