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Almost-sure global existence in the Newtonian N-body problem
Prove that for Newtonian point masses, the initial conditions whose motion breaks down in finite time form a set of measure zero.
| 1 | { |
| 2 | "domain": "physics-astronomy", |
| 3 | "topics": [ |
| 4 | "mathematical-physics", |
| 5 | "celestial-mechanics" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "source": { |
| 9 | "key": "simon-problems", |
| 10 | "name": "Simon's problems in mathematical physics", |
| 11 | "url": "https://en.wikipedia.org/wiki/Simon_problems#The_1984_list", |
| 12 | "id": "1984-1A", |
| 13 | "curator": "Barry Simon", |
| 14 | "poser": "Barry Simon", |
| 15 | "status": "open", |
| 16 | "as_of": "2026-10-20", |
| 17 | "catalog": "0521c19bbd38" |
| 18 | }, |
| 19 | "review": true, |
| 20 | "approval": "first-time" |
| 21 | } |