scholarly journals Remarks on regularity criteria for axially symmetric weak solutions to the Navier-Stokes equations

2011 ◽  
Vol 35 (3) ◽  
pp. 360-371 ◽  
Author(s):  
Adam Kubica ◽  
Milan Pokorný ◽  
Wojciech Zajączkowski
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations

Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations

2011 ◽  
Vol 52 (5) ◽  
pp. 053103 ◽  
Author(s):  
Zujin Zhang ◽  
Zheng-an Yao ◽  
Ming Lu ◽  
Lidiao Ni
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

2016 ◽  
Vol 18 (06) ◽  
pp. 1650018 ◽  
Author(s):  
Wei Ren ◽  
Yanqing Wang ◽  
Gang Wu
Keyword(s):  
Weak Solutions ◽  
Partial Regularity ◽  
Morrey Space ◽  
Stokes Equations ◽  
Mhd Equations ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Mixed Norm ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in [Formula: see text] for [Formula: see text]. In comparison with the work of the 3D fractional Navier–Stokes equations obtained by Tang and Yu in [Partial regularity of suitable weak solutions to the fractional Navier–Stokes equations, Comm. Math. Phys. 334 (2015) 1455–1482], our results include their endpoint case [Formula: see text] and the external force belongs to a more general parabolic Morrey space. Moreover, we prove some interior regularity criteria just via the scaled mixed norm of the velocity for the suitable weak solutions to the fractional MHD equations.

scholarly journals On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations

2019 ◽  
Vol 21 (4) ◽  
Author(s):  
Joanna Rencławowicz ◽  
Wojciech M. Zaja̧czkowski
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Radial Component ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Angular Component ◽  
Regularity Of Weak Solutions ◽  
Axisymmetric Solutions

Abstract We point out some criteria that imply regularity of axisymmetric solutions to Navier–Stokes equations. We show that boundedness of $$\Vert {v_{r}}/{\sqrt{r^3}}\Vert _{L_2({\mathbb {R}}^3\times (0,T))}$$‖vr/r3‖L2(R3×(0,T)) as well as boundedness of $$\Vert {\omega _{\varphi }}/{\sqrt{r}} \Vert _{L_2({\mathbb {R}}^3\times (0,T))}$$‖ωφ/r‖L2(R3×(0,T)), where $$v_r$$vr is the radial component of velocity and $$\omega _{\varphi }$$ωφ is the angular component of vorticity, imply regularity of weak solutions.

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