Viscosity solutions and hyperbolic motions: a new PDE method for the N-body problem

• 成果类型: Article
• 署名作者: Maderna, Ezequiel; Venturelli, Andrea
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.192.2.5
• 发表日期: 2020
• 页码: 499-550
• 关键词: Existence; configurations; FINITENESS; minimizers

摘要

We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h > 0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x, clu) = h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marchal's Theorem, whose main use in recent literature has been to prove the existence of periodic orbits.