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arXiv · 1607.08345

Partial regularity of Solutions of Navier-Stokes equations

Xixia Ma
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Abstract

In this paper, we study the singular set of 3-dimensional Navier-Stokes equations. Under the condition$\frac{1}{R^{\frac{3s}{q}+2-s}}\int^{R^{2}}_{0}(\int_{B_{R}}|u|^{q}dx)^{\frac{s}{q}}ds <C,$ for $(q,s)\in\{(2,5),(5,2)\},$ we use the backward uniqueness of parabolic equations to show that the Hausdorff dimension of the singular set is less than 1.

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Xixia Ma. 2016-07-28. Partial regularity of Solutions of Navier-Stokes equations. https://arxiv.org/abs/1607.08345

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