The manuscript reports smooth compactly supported divergence-free initial data on R³ whose unforced three-dimensional incompressible Euler solution has finite maximal lifespan, with unbounded velocity gradient and divergent time integral of maximum vorticity.
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The manuscript reports smooth compactly supported divergence-free initial data on R³ whose unforced three-dimensional incompressible Euler solution has finite maximal lifespan, with unbounded velocity gradient and divergent time integral of maximum vorticity.
Read original source Original Euler manuscript, Theorem 1.1cdn.openai.com
Original report: 2026-09-08The manuscript reports smooth compactly supported divergence-free initial data on R³ whose unforced three-dimensional incompressible Euler solution has finite maximal lifespan, with unbounded velocity gradient and divergent time integral of maximum vorticity.
If correct, resolves the smooth whole-space unforced Euler finite-time breakdown target, beyond forced or lower-regularity variants.
A sourced result with the exact hypotheses, baseline, and AI role stated; verification is assessed separately.
Background review: 2026-10-11. Selected sources:
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