Minor correction: OpenAI’s solution does not address the “smoothness problem”; this article states they solved the existence and smoothness problem. They claim to have solved parts (C) and (D) of the Millenium prize statement, but the smoothness problem refers to part (A).
“The first statement (A), which is known as the "smoothness" problem, states that there should always exist smooth and globally defined solutions to the Navier–Stokes equations in three-dimensional space. The second statement (C), known as the "breakdown" problem, states that there should be at least one set of initial conditions and external forces for which there are no smooth solutions to the Navier–Stokes equations.“
Edit: Though I notice now the OpenAI blogpost does claim to solve the “smoothness and existence problem”, so maybe there’s simply terminology differences here. I’ll note many mathematicians such as Dennis Sullivan suggest part (A) is the more important part.
Minor correction: OpenAI’s solution does not address the “smoothness problem”; this article states they solved the existence and smoothness problem. They claim to have solved parts (C) and (D) of the Millenium prize statement, but the smoothness problem refers to part (A).
See https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_sm...
“The first statement (A), which is known as the "smoothness" problem, states that there should always exist smooth and globally defined solutions to the Navier–Stokes equations in three-dimensional space. The second statement (C), known as the "breakdown" problem, states that there should be at least one set of initial conditions and external forces for which there are no smooth solutions to the Navier–Stokes equations.“
Edit: Though I notice now the OpenAI blogpost does claim to solve the “smoothness and existence problem”, so maybe there’s simply terminology differences here. I’ll note many mathematicians such as Dennis Sullivan suggest part (A) is the more important part.
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