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Remarks on regularity criteria for the Navier–Stokes equations with axisymmetric data

Volume 117 / 2016

Zujin Zhang Annales Polonici Mathematici 117 (2016), 181-196 MSC: Primary 35B65; Secondary 35Q35, 76D03. DOI: 10.4064/ap3856-3-2016 Published online: 8 July 2016


We consider the axisymmetric Navier–Stokes equations with non-zero swirl component. By invoking the Hardy–Sobolev interpolation inequality, Hardy inequality and the theory of $A_\beta \ (1 \lt \beta \lt \infty )$ weights, we establish regularity criteria involving $u^r$, $\omega ^z$ or $\omega ^\theta $ in some weighted Lebesgue spaces. This improves many previous results.


  • Zujin ZhangSchool of Mathematics and Computer Sciences
    Gannan Normal University
    Ganzhou 341000, Jiangxi, P.R. China

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