On partial regularity of steady-state solutions to the 6D Navier-Stokes equations

Details On partial regularity of steady-state solutions to the 6D Navier-Stokes equations On partial regularity of steady-state solutions to the 6D Navier-Stokes equations

2011-01-28

arxiv.org/abs/1101.5580v2

Mathematics

Analysis of PDEs

19 pages, revised version, to appear in Indiana Univ. Math. J

Scientific paper

Consider steady-state weak solutions to the incompressible Navier-Stokes
equations in six spatial dimensions. We prove that the 2D Hausdorff measure of
the set of singular points is equal to zero. This problem was mentioned in 1988
by Struwe [24], during his study of the five dimensional case.

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