Communications in Mathematical Physics

, Volume 110, Issue 4, pp 525–551 | Cite as

Nearly one dimensional singularities of solutions to the Navier-Stokes inequality

  • Vladimir Scheffer
Article

Abstract

There exists a functionu satisfying (1)u is a weak solution to the Navier-Stokes equations of incompressible fluid flow in three-space with an external force that reduces the speed at every point, (2) the internal singularities ofu have Hausdorff dimension close to 1.

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References

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    Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier-Stokes equations. Commun. Pure Appl. Math.35, 771–831 (1982)Google Scholar
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    Moran, P. A. P.: Additive functions of intervals and Hausdorff measure. Proc. Camb. Phil. Soc.42, 15–23 (1946)Google Scholar
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    Scheffer, V.: Hausdorff measure and the Navier-Stokes equations. Commun. Math. Phys.55, 97–112 (1977)Google Scholar
  4. 4.
    Scheffer, V.: A solution to the Navier-Stokes inequality with an internal singularity. Commun. Math. Phys.101, 47–85 (1985)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Vladimir Scheffer
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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