{
  "id": 5831022,
  "title": "Finite time blowup for an averaged three-dimensional Navier-Stokes equation",
  "url": "https://urgent.news/2026/09/05/finite-time-blowup-for-an-averaged-three-dimensional-navier-stokes",
  "topic": "science",
  "section": "Science",
  "published": "2026-09-05T20:25:59.000Z",
  "source": {
    "name": "Hacker News",
    "slug": "hacker-news",
    "url": "https://terrytao.wordpress.com/2014/02/04/finite-time-blowup-for-an-averaged-three-dimensional-navier-stokes-equation/"
  },
  "original_language": "en",
  "account": "The research paper titled \"Finite time blowup for an averaged three-dimensional Navier-Stokes equation\" has been published in the Journal of the American Mathematical Society. The authors aim to address the long-standing problem of global regularity in the Navier-Stokes equations by constructing a modified version of the equations that still satisfies many of the original nonlinearity and energy identity properties, but allows for solutions that become unbounded in a finite amount of time. This is significant because previous attempts to prove global regularity for the Navier-Stokes equations relied solely on upper bound estimates of the nonlinearity and the energy identity, neither of which are applicable to the modified equations. The authors introduce a new averaged bilinear operator, which is a finite linear combination of local cascade operators, and demonstrate that this modified Navier-Stokes equation admits solutions that blow up in finite time. This result provides a significant obstacle to any attempt to prove global regularity for the true Navier-Stokes equations using only the energy identity and upper bound estimates for the nonlinearity.",
  "summary": null,
  "key_points": [
    "Researchers publish paper on finite time blowup for modified Navier-Stokes equation",
    "Modified equations allow solutions to become unbounded in finite time",
    "New averaged bilinear operator demonstrates blowup in finite time"
  ],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}