State of Proof

Mathematical claim · candidate · examination not started

Blowup for the Euler Equations with Smooth Forcing

Levent Alpöge; Tristan Buckmaster.

Source date: 2026-09-08 · Added: 2026-09-08 · Record updated:

Inclusion is not validation. This is an intake record and proposed check plan, not a completed examination or a peer-review decision. Any separate docket states its own exact source and scope.

Candidate · added · paper-2026-09-08-blowup-for-the-euler-equations-with-smooth-forcing

A smooth push can still produce extreme fluid structure

What it is
The paper claims smooth forcing can produce unbounded twisting and gradients in three-dimensional ideal-fluid flow.
Who did it
Levent Alpöge and Tristan Buckmaster
What it could mean
A smooth push does not necessarily mean a smooth ride. This claim would show an ideal fluid model developing unbounded twisting under smoothly applied forces—not real water reaching infinite speed.

Examination not started

See the check plan

Evidence & validation

From announcement to evidence

Discovery recorded. State of Proof has not yet examined this claim.

  1. Read the original work

    Blowup for the Euler Equations with Smooth Forcing ↗

    Levent Alpöge; Tristan Buckmaster.

  2. See the proposed checks

    Are the force's space-time smoothness and the stated uniqueness class preserved throughout the analytic-to-formal translation?

  3. No proof docket yet

    A docket is the public record of checks and open questions. This paper does not have one yet; the check plan above describes work still to do.

    Explore existing proof dockets →
How validation works →
What it claims
The paper claims finite-time blowup of vorticity and circulation gradients in three-dimensional incompressible Euler flow with a force smooth in space and time, including at the terminal time.
Why this could matter
A smooth push can still produce extreme fluid structure A smoothly applied force need not keep an ideal fluid smooth forever. The authors claim a flow whose twisting and gradients become unbounded. This is about a mathematical limit, not proof that real water reaches infinite speed.
If it holds up
It would strengthen our understanding of singularity formation under smooth forcing and provide a construction to study related equations.
If it does not
A failed estimate or translation would locate what must be repaired before relying on the claimed smooth-forcing result.
Impact horizon
Foundational · Fluid models · Mathematical physics · AI-assisted proof
Version
Public manuscript retrieved 2026-09-08; PDF SHA-256 97ef408bff09b4f6ed9f3867734d1eb2245f3f34e6334b28136c84c02d0ae8d8. Discovery date is not a claim of first publication.
Why we tracked it
The September 8 fluid-mathematics announcements warrant distinct intake records for each equation, forcing assumption and proof-completion state.
Highest-risk dependency
Forced Euler, not unforced Euler or Navier–Stokes. The authors report formal verification; State of Proof has not replayed it. Authorship follows the authors' statement; the inspected Euler PDF has no byline on its first page.
Available artifacts
A public formal-source repository is linked: https://github.com/tristanbuckmaster/fluidlean. The authors describe extensive Claude and Codex assistance within a human-directed program building on Córdoba and Martínez-Zoroa. No manuscript-linked code was executed; source availability is not proof verification.
Current boundary
Intake record only; examination not started.

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