A N-body problem with weak force potential through Hamilton-Jacobi equation approach
Analysis of PDEs
2022-05-13 v1 Dynamical Systems
Abstract
This paper we consider for the N-body problem with potential 1/r{\alpha} (0 < {\alpha} < 1) the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. Here E is the Euclidean space where the bodies moving and is the norm induced by the inner product. The energy level h > 0 of the motion can also be chosen arbitrarily. We use the global viscosity solutions for the Hamilton-Jacobi equation H (x, dxu) = h and geodesics.
Cite
@article{arxiv.2205.05942,
title = {A N-body problem with weak force potential through Hamilton-Jacobi equation approach},
author = {Putian Yang and Shiqing Zhang},
journal= {arXiv preprint arXiv:2205.05942},
year = {2022}
}