Let u be a Leray-Hopf weak solution to the Navier-Stokes equations. We will show that the set of possible singular points of the vector field resulting from integrating the velocity u with respect to time has Hausdorff dimension zero.
Submitted November 24, 2006. Published August 28, 2008.
Math Subject Classifications: 35Q76D
Key Words: Partial regularity; Navier-Stokes equations; Leray-Hopf weak solution.
An addendum was posted on September 30, 2008. It modifies the proof of the main theorem. Please see the last page of this manuscript.
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| Cheng He |
Institute of Applied Mathematics
Academy of Mathematics and Systems Science
Academia Sinica, Beijing, 100080, China
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