{
  "video_id": "reddit_1wb05u0",
  "channel_slug": "singularity",
  "channel_handle": "r/singularity",
  "title": "Chris Combs, professor of Aerospace engineering, throws some cold water on OpenAI’s NS solution",
  "url": "https://www.reddit.com/r/singularity/comments/1wb05u0/chris_combs_professor_of_aerospace_engineering/",
  "external_url": null,
  "upload_date": "20260908",
  "published_at": "2026-09-08T20:29:40+00:00",
  "transcript": "“Some thoughts on the Navier-Stokes news from a professor of aerospace engineering:  \n1) take a deep breath  \n2) posts indicating we \"solved Navier-Stokes\" are incorrect and overblown. A very specific mathematical proof involving a niche scenario for Navier-Stokes has \\*potentially\\* been shown (that a perfectly smooth incompressible initial condition with finite energy could produce a singularity--note the assumptions here piled on to an equation set that already involves some assumptions).  \n3) there is no general closed form solution for N-S and that's not what this news is about  \n4) this is more of a mathematical curiosity than anything else and could matter a lot to mathematicians but basically changes nothing in the way N-S are used in practice  \n5) there are already very useful exact solutions to Navier-Stokes that greatly simplify the equation set with the right boundary conditions/geometry like laminar flow through a pipe or a 2D Taylor-Green vortex  \n6) in aerospace, we already treat N-S as an approximation in many instances and are well aware of its limitations. we don't outright solve these equations anyway and regularly chop off terms or simplify parts (at the expense of accuracy) to make them easier to deal with.  \n7) to be honest I have never found this specific problem to be particularly interesting because we know a core assumption of N-S is a \"continuum\" fluid where you ignore molecules and assume hydrodynamic scales >>> molecular scales. We know a real fluid cannot have infinite velocity or energy. But clearly you can push equations outside of their bound of validity and make them produce funky results and singularities.”\n\nhttps://x.com/drchriscombs/status/2097409234321154547?s=46\n\n\n\n--- Top Comments ---\n\n\n[190 upvotes] “AIs not getting better, the millennial prize was trivial this whole time” \n\n[160 upvotes] There has been a huge amount of misunderstanding on all this. Saying \"We solved Navier-Stokes\" could mean two completely different things.\n\n1. It could mean solving the Navier-Stokes equations. This is likely impossible. Dynamical equations in general just do not admit general analytical solutions. They can become chaotic. However, they can sometimes be solved given very specific boundary conditions.\n2. It could mean solving the Navier–Stokes existence and smoothness Millennium prize problem. This means proving or disproving that certain boundary conditions can lead to a singularity in finite time.\n\nAll the parties involved are very clear that it's the 2nd problem that's been solved, ie, the existence and smoothness conjecture has been DISproved. This is a huge theoretical advance but I doubt it has any practical application. It just means that under certain very specific conditions, the Navier-Stokes equations are not physically realistic. It's not going to help you design a new aircraft or whatever people are saying. Under all the physical circumstances for which N-S is relevant, it's still relevant and we'll continue as usual unless there's some other advance.\n\nSo this person sa\n\n[79 upvotes] ![gif](giphy|WwWTfQuCZ448psk1qB)\n\n[67 upvotes] > a niche scenario for Navier-Stokes\n\nAka the scenario that the Millennium Problem is based off of",
  "transcript_chars": 3221,
  "ingested_at": "2026-09-09T01:30:20.254027+00:00",
  "source": "reddit",
  "yt_meta": {
    "score": 224,
    "upvote_ratio": 0.8,
    "num_comments": 142,
    "author": "Mindrust",
    "is_self": true
  }
}