Caffarelli, Kohn and Nirenberg: partial regularity for Navier-Stokes weak solutions

What changed

Established a parabolic Hausdorff-measure bound on the singular set of suitable three-dimensional weak solutions.

Scientific scope

The record is the exact three-author 1982 paper. It is a partial-regularity result for suitable weak solutions under the paper's hypotheses, not a proof of global smoothness, uniqueness or the full Navier-Stokes Millennium problem.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact three-author 1982 paper. It is a partial-regularity result for suitable weak solutions under the paper's hypotheses, not a proof of global smoothness, uniqueness or the full Navier-Stokes Millennium problem.

Contributors

• Luis A. Caffarelli · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
• Robert V. Kohn · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
• Louis Nirenberg · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Wiley page for the Caffarelli-Kohn-Nirenberg paper
• ADS record for the Caffarelli-Kohn-Nirenberg paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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