Home Problems Navier–Stokes existence and smoothness Research history Selected research history · publication v4
Navier–Stokes existence and smoothness Follow the ideas, results and limitations over time. This is a selected history, not a complete literature survey or a measure of how close the problem is to being solved.
Current state & remaining question → Viewing the timeline from pinned publication v4.
5 selected milestones · Source coverage checked 2026-10-13 · Historical annotation and mathematical review remain separate.
2000 publication
Foundation
Four official existence/breakdown alternatives Fefferman specifies decay, periodicity, forcing and energy hypotheses for the Millennium question.
Scope & review: The four alternatives must not be collapsed into one unqualified regularity assertion.
Statements & sources Historical annotation review: pending. The date refers to the publication, with the precision supported by the source.
Sep 5, 2026 announcement
Proposal
A forced breakdown argument is produced OpenAI’s later announcement dates its model-produced Navier–Stokes argument to 5 September.
Scope & review: This is a first-party account of discovery; public release and formal checking are later events.
Statements & sources Historical annotation review: pending. The date refers to the announcement, with the precision supported by the source.
Sep 8, 2026 announcement
Proposal
Manuscript and formal source released The public report gives a whole-space theorem and periodic corollary for every positive viscosity.
Scope & review: It uses external forcing and does not establish unforced viscous blowup.
Statements & sources Historical annotation review: pending. The date refers to the announcement, with the precision supported by the source.
Sep 10, 2026 formalization
Formalization
Pinned formal proof revision The formal project exposes the exact C/D statements and self-assessed metadata.
Scope & review: This is a repository revision date, not a new discovery or an OpenMath execution.
Statements & sources Historical annotation review: pending. The date refers to the formalization, with the precision supported by the source.
Sep 11, 2026 assessment
Assessment
CMI acknowledges the announcement The Institute states that evaluation will follow its deliberately unhurried process.
Scope & review: The announcement records no prize award or completed evaluation.
Statements & sources Historical annotation review: pending. The date refers to the assessment, with the precision supported by the source.
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