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.
See the check plan
Evidence & validation
From announcement to evidence
Discovery recorded. State of Proof has not yet examined this claim.
Read the original work
Blowup for the Euler Equations with Smooth Forcing ↗See the proposed checks
Are the force's space-time smoothness and the stated uniqueness class preserved throughout the analytic-to-formal translation?
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 →
- 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.