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

Abstract

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.

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

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