Abstract
We establish some interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations which allow the vertical part of the velocity to be large under the local scaling invariant norm. As an application, we improve Ladyzhenskaya-Prodi-Serrin’s criterion and Escauriza-Seregin-Šverák’s criterion. We also show that if a weak solution u satisfies
for some 3 < p < ∞, then the number of singular points is finite.
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Wendong Wang is supported by the Fundamental Research Funds for the Central Universities.
Zhifei Zhang is partly supported by NSF of China under Grant 10990013 and 11071007.
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Wang, W., Zhang, Z. On the interior regularity criteria and the number of singular points to the Navier-Stokes equations. JAMA 123, 139–170 (2014). https://doi.org/10.1007/s11854-014-0016-7
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DOI: https://doi.org/10.1007/s11854-014-0016-7