Electron. J. Diff. Eqns., Vol. 2008(2008), No. 120, pp. 1-6.

Remark on the spatial regularity for the Navier-Stokes equations

Cheng He

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
email: chenghe@amss.ac.cn

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