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Abstract and Applied Analysis
Volume 2012, Article ID 184674, 9 pages
Research Article

A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space

School of Science, Tianjin Polytechnic University, Tianjin 300387, China

Received 3 July 2012; Accepted 7 August 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Xunwu Yin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the regularity of Leray weak solutions to the 3D Navier-Stokes equations in Lorentz space. It is proved that the weak solution is regular if the horizontal velocity denoted by ̃𝑒=(𝑒1,𝑒2,0) satisfies ̃𝑒(π‘₯,𝑑)βˆˆπΏπ‘ž(0,𝑇;𝐿𝑝,∞(𝐑3))for2/π‘ž+3/𝑝=1,3<𝑝<∞. The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space.