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Navier-Stokes equations

Topic

Heard in 22 episodes across 20 shows since Jun 2026

The Navier–Stokes equations are a system of nonlinear partial differential equations that describe the motion of viscous fluids, expressing conservation of mass and momentum while accounting for quantities such as velocity, pressure, density, and viscosity. They underpin mathematical and computational modeling of fluid flow; a famous unresolved question asks whether smooth, physically meaningful solutions in three dimensions can develop singularities (finite-time blow-up), which is why claims that AI has “solved Navier–Stokes” refer to a major mathematical or computational result rather than to a namesake.

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Discussed inAI & Tech58%Health & Science42%

Episodes

22
across 20 shows

This week

0
episodes on 0 shows

Expert statements

9
4 positive · 4 negative

Share of the conversation

Mentions of Navier-Stokes equations per 1,000 mentions of anything, 7-day rolling, across the podcasts PodLume Trends follows.

0.0‰0.05‰0.1‰0.15‰Aug 15Sep 6Sep 29Oct 21Nov 12
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Sep 80.03‰3
Sep 120.04‰1
Sep 140.05‰1
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Oct 190.14‰1
Oct 260.01‰1
Oct 290.02‰1
Nov 40.02‰1
Nov 70.02‰1

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What experts have said about Navier-Stokes equations

9 statements · 4 positive · 4 negative · 1 mixed

  1. Justin SolomonPositiveOct 9, 2026· Odd Lots

    Navier–Stokes equations model fluid motion over time.

    “the Navier-Stokes equations were this model. They go back quite a long time that explain the motion of, for example, liquid in a cup.”

    Listen at 18:21

    Open the episode · How AI Is Upending the World of Mathematics
  2. Justin SolomonNegativeOct 9, 2026· Odd Lots

    The reported Navier–Stokes proof had not yet received official verification.

    “their proof has not been officially verified and checked.”

    Listen at 43:51

    Open the episode · How AI Is Upending the World of Mathematics
  3. Justin SolomonMixedOct 9, 2026· Odd Lots

    The Navier–Stokes proof is probably correct but probably not elegant.

    “Is it elegant? Probably not. Is it correct? Yes, probably.”

    Listen at 48:58

    Open the episode · How AI Is Upending the World of Mathematics
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Statements are attributed to the speaker as said on the episode and reflect their view at the time, not PodLume's. They are not advice.

Episodes

22 episodes featuring Navier-Stokes equations, newest first

See all 22 episodes →