Nearly one dimensional singularities of solutions to the Navier-Stokes inequality
- 64 Downloads
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.
Unable to display preview. Download preview PDF.
- 1.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
- 2.Moran, P. A. P.: Additive functions of intervals and Hausdorff measure. Proc. Camb. Phil. Soc.42, 15–23 (1946)Google Scholar
- 3.Scheffer, V.: Hausdorff measure and the Navier-Stokes equations. Commun. Math. Phys.55, 97–112 (1977)Google Scholar
- 4.Scheffer, V.: A solution to the Navier-Stokes inequality with an internal singularity. Commun. Math. Phys.101, 47–85 (1985)Google Scholar