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
Article

Abstract

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.

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References

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    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

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