Communications in Mathematical Physics

, Volume 101, Issue 1, pp 47–85

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

  • Vladimir Scheffer

DOI: 10.1007/BF01212356

Cite this article as:
Scheffer, V. Commun.Math. Phys. (1985) 101: 47. doi:10.1007/BF01212356


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.

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

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