Global existence and singularity of the Hill's type lunar problem with strong potential

TL;DR

This paper investigates the long-term behavior and potential singularities in Hill's lunar problem with strong potential, using PDE ground state concepts to analyze solution dynamics relative to energy thresholds.

Contribution

It introduces a novel approach by applying PDE ground state ideas to characterize solution fate in Hill's lunar problem, including the definition of relative equilibrium as a ground state.

Findings

Solutions below ground state energy tend to global existence.

Solutions at or above ground state energy may develop singularities.

The analysis provides energetic criteria for solution behavior.

Abstract

We characterize the fate of the solutions of Hill's type lunar problem using the ideas of ground states from PDE. In particular, the relative equilibrium will be defined as the ground state, which satisfies some crucial energetic variational properties in our analysis. We study the dynamics of the solutions below, at, and (slightly) above the ground state energy threshold.