Communications in Mathematical Physics

, Volume 73, Issue 1, pp 1–42

The Navier-Stokes equations on a bounded domain

  • Vladimir Scheffer

DOI: 10.1007/BF01942692

Cite this article as:
Scheffer, V. Commun.Math. Phys. (1980) 73: 1. doi:10.1007/BF01942692


SupposeU is an open bounded subset of 3-space such that the boundary ofU has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solutionu to the time dependent Navier-Stokes equations of incompressible fluid flow inU such that the curl ofu is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite.

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

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