On some regularity criteria for axisymmetric Navier-Stokes equations

Joanna Renc{\l}awowicz; Wojciech M. Zaj\k{a}czkowski

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On some regularity criteria for axisymmetric Navier-Stokes equations

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arxiv 1806.07145 v1 pith:FNA7W5IE submitted 2018-06-19 math.AP

On some regularity criteria for axisymmetric Navier-Stokes equations

Joanna Renc{\l}awowicz , Wojciech M. Zaj\k{a}czkowski This is my paper

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keywords regularityaxisymmetricboundednesscomponentcriteriaequationsimplynavier-stokes

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We point out some criteria that imply regularity of axisymmetric solutions to Navier-Stokes equations. We show that boundedness of $\|{v_{r}}/{\sqrt{r^3}}\|_{L_2({\rm R}^3\times (0,T))}$ as well as boundedness of $\|{\omega_{\varphi}}/{\sqrt{r}}\|_{L_2({\rm R}^3\times (0,T))},$ where $v_r$ is the radial component of velocity and $\omega_{\varphi}$ is the angular component of vorticity, imply regularity of weak solutions.

On some regularity criteria for axisymmetric Navier-Stokes equations

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