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

Zujin Zhang

Zujin Zhang

Annales Polonici Mathematici, Tome 116 (2016), p. 181-196 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $* A_{β}$ (1 < β < ∞) weights, we establish regularity criteria involving $u^{r}$ , $ω^{z}$ or $ω^{θ}$ in some weighted Lebesgue spaces. This improves many previous results.

Publié le : 2016-01-01

Zbl 06622314

EUDML-ID : urn:eudml:doc:286447

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     author = {Zujin Zhang},
     title = {Remarks on regularity criteria for the Navier-Stokes equations with axisymmetric data},
     journal = {Annales Polonici Mathematici},
     volume = {116},
     year = {2016},
     pages = {181-196},
     zbl = {06622314},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3856-3-2016}
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Zujin Zhang. Remarks on regularity criteria for the Navier-Stokes equations with axisymmetric data. Annales Polonici Mathematici, Tome 116 (2016) pp. 181-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3856-3-2016/