Remarks on regularity criteria for axially symmetric weak solutions to the Navier–Stokes equations

Adam Kubica, Milan Pokorný, Wojciech M. Zajączkowski

Type: Article

Publication Date: 2011-12-29

Citations: 34

DOI: https://doi.org/10.1002/mma.1586

Abstract

We examine the conditional regularity of the solutions to the Navier–Stokes equations in the entire three‐dimensional space under the assumption that the data are axially symmetric. We show that if a radial or angular component of velocity satisfies a weighted Serrin condition, then the solution is regular. Copyright © 2011 John Wiley & Sons, Ltd.

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
Mathematical Methods in the Applied Sciences - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	A Regularity Criterion for Positive Part of Radial Component in the Case of Axially Symmetric Navier-Stokes Equations	2015	Adam Kubica
+ PDF Chat	A regularity criterion for axially symmetric solutions to the Navier–Stokes equations	2011	Wojciech M. Zajączkowski
+	Remarks on Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier Stokes Equations	2010	Adam Kubica
+ PDF Chat	Regularity criteria with angular integrability for the Navier–Stokes equation	2014	Renato Lucà
+	A REGULARITY CRITERION FOR THE ANGULAR VELOCITY COMPONENT IN AXISYMMETRIC NAVIER-STOKES EQUATIONS	2007	Rej Kreml
+ PDF Chat	A Sufficient Condition of Regularity for Axially Symmetric Solutions to the Navier–Stokes Equations	2007	G. Serëgin Wojciech M. Zajączkowski
+	Regularity criteria with angular integrability for the Navier-Stokes equation	2013	Renato Lucà
+	Regularity criteria with angular integrability for the Navier-Stokes equation	2013	Renato Lucà
+	A regularity criterion for the angular velocity component in axisymmetric Navier-Stokes equations	2007	Ondřej Kreml Milan Pokorný
+	On weighted regularity criteria for the axisymmetric Navier–Stokes equations	2016	Zujin Zhang
+	Navier–Stokes equations with regularity in one directional derivative of the pressure	2014	Zujin Zhang
+	A sufficient condition of regularity for axially symmetric solutions to the Navier-Stokes equations	2007	Grigory Seregin Wojciech M. Zajączkowski
+ PDF Chat	A Note on Local Regularity of Axisymmetric Solutions to the Navier–Stokes Equations	2022	G. Serëgin
+ PDF Chat	Some Remarks on regularity criteria of Axially symmetric Navier-Stokes equations	2018	Zijin Li Xinghong Pan
+	An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier—Stokes Equations	2000	Jiřı́ Neustupa Milan Pokorný
+	Some Remarks on Regularity Criteria of Axially Symmetric Navier-Stokes Equations	2018	Zijin Li Xinghong Pan
+	Regularity criteria for the Navier–Stokes equations in terms of the velocity direction and the flow of energy	2022	Zhengguang Guo Petr Kučera Zdeněk Skalák
+	Regularity criterion of axisymmetric weak solutions to the 3D Navier–Stokes equations	2006	Qionglei Chen Zhifei Zhang
+ PDF Chat	Conditional regularity for the Navier–Stokes–Fourier system with Dirichlet boundary conditions	2023	Danica Basarić Eduard Feireisl Hana Mizerová
+	Regularity criterion to the axially symmetric Navier–Stokes equations	2015	Dongyi Wei

Works That Cite This (33)

Action	Title	Year	Authors
+	Regularity of the 3D Navier–Stokes equations with viewpoint of 2D flow	2017	Hyeong‐Ohk Bae
+	Weighted a priori estimates for the swirl component of the vorticity of the axisymmetric Navier–Stokes system	2020	Zujin Zhang Sinan Wang
+	Critical regularity criteria for Navier-Stokes equations in terms of one directional derivative of the velocity	2020	Hui Chen Daoyuan Fang Ting Zhang
+ PDF Chat	A Regularity Criterion for Positive Part of Radial Component in the Case of Axially Symmetric Navier-Stokes Equations	2015	Adam Kubica
+ PDF Chat	Global Strong Solutions to the Inhomogeneous Incompressible Navier--Stokes System in the Exterior of a Cylinder	2021	Zhengguang Guo Yun Wang Chunjing Xie
+	A regularity criterion for the 3D axisymmetric Boussinesq equations with non-zero swirl	2023	Peng Wang Zhengguang Guo
+	Global Axisymmetric Solutions to the 3D MHD Equations with Nonzero Swirl	2022	Peng Wang Zhengguang Guo
+	Regularity criterion to the axially symmetric Navier–Stokes equations	2015	Dongyi Wei
+	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mn>3</mml:mn></mml:math>D axisymmetric MHD system with regularity in the swirl component of the vorticity	2017	Zujin Zhang Zheng‐an Yao
+	Muliti-scale regularity of axisymmetric Navier-Stokes equations	2018	Daoyuan Fang Hui Chen Ting Zhang

Works Cited by This (25)

Action	Title	Year	Authors
+ PDF Chat	Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations	2002	Luigi C. Berselli Giovanni P. Galdi
+	On the result of He concerning the smoothness of solutions to the Navier-Stokes equations	2003	Milan Pokorný
+	One component regularity for the Navier–Stokes equations	2005	Igor Kukavica Mohammed Ziane
+ PDF Chat	A New Regularity Criterion for the Navier-Stokes Equations in Terms of the Gradient of One Velocity Component	2002	Yong Zhou
+	An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier—Stokes Equations	2000	Jiřı́ Neustupa Milan Pokorný
+ PDF Chat	A regularity criterion for axially symmetric solutions to the Navier–Stokes equations	2011	Wojciech M. Zajączkowski
+ PDF Chat	On Axially Symmetric Flows in $mathbb R^3$	1999	Salvatore Leonardi Josef Málek Jindřich Nečas Milan Pokorný
+	Generic Solvability of the Axisymmetric 3-D Euler Equations and the 2-D Boussinesq Equations	1999	Dongho Chae Oleg Imanuvilov
+ PDF Chat	Some New Regularity Criteria for the Navier-Stokes Equations Containing Gradient of the Velocity	2004	Patrick Penel Milan Pokorný
+	Regularity criteria for the three-dimensional Navier-Stokes equations	2008	Chongsheng Cao Edriss S. Titi