Communications in Mathematical Physics

, Volume 101, Issue 1, pp 47–85 | Cite as

A solution to the Navier-Stokes inequality with an internal singularity

  • Vladimir Scheffer


We consider weak solutions to the time dependent Navier-Stokes equations of incompressible fluid flow in three dimensional space with an external force that always acts against the direction of the flow. We show that there exists a solution with an internal singularity. The speed of the flow reaches infinity at this singular point. In addition, the solution has finite kinetic energy.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math.35, 771–831 (1982)Google Scholar
  2. 2.
    Conte, S.D., de Boor, C.: Elementary numerical analysis, an algorithmic approach, 3rd ed. New York: McGraw-Hill 1980Google Scholar
  3. 3.
    Federer, H.: Geometric measure theory. Berlin, Heidelberg, New York: Springer 1969Google Scholar
  4. 4.
    Scheffer, V.: Hausdorff measure and the Navier-Stokes equations. Commun. Math. Phys.55, 97–112 (1977)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

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

Personalised recommendations