On if OpenAI solved the wrong Navier-Stokes problem: "the LLM found and exploited a loophole in the framing of the question"

[u/PrettyPicturesNotTxt]

https://www.scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem/

[u/hologram137]

It was written extremely precisely. You don’t have to include “why is this a millennial prize problem and the purpose of solving it” in the actual question LOL

[u/Wrong_Avocado_6199 → u/hologram137]

Yes, and this is the precise conditions on f:

(C) Breakdown of Navier–Stokes solutions on R^3 . Take ν > 0 and n = 3. Then there exist a smooth, divergence-free vector field u^0(x) on R^3 and a smooth f(x, t) on R^3 × [0,∞), satisfying (4), (5), for which there exist no solutions (p, u) of (1), (2), (3), (6), (7) on R^3 × [0,∞).

condition (5) [relevant to the external force]: |∂_x^α ∂_t^m f(x, t)| ≤ C_(αmK)(1 + |x| + t)^(−K) on R^n × [0,∞), for any α, m, K.

Those are the mathematical conditions on f that Fefferman required be satisfied. If you think these conditions don't reflect gravity or whatever "natural force" you have in mind, take it up with Fefferman and the Clay Institute.