# American Institute of Mathematical Sciences

September  2013, 6(3): 545-556. doi: 10.3934/krm.2013.6.545

## Logarithmically improved regularity criteria for the generalized Navier-Stokes and related equations

 1 Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037 2 Faculty of Mathematics and and Mathematical Research Center, for Industrial Technology, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan 3 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang

Received  November 2012 Revised  February 2013 Published  May 2013

In this paper, logarithmically improved regularity criteria for the generalized Navier-Stokes equations are established in terms of the velocity, vorticity and pressure, respectively. Here $BMO$, the Triebel-Lizorkin and Besov spaces are used, which extend usual Sobolev spaces much. Similar results for the quasi-geostrophic flows and the generalized MHD equations are also listed.
Citation: Jishan Fan, Yasuhide Fukumoto, Yong Zhou. Logarithmically improved regularity criteria for the generalized Navier-Stokes and related equations. Kinetic & Related Models, 2013, 6 (3) : 545-556. doi: 10.3934/krm.2013.6.545
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