On the interior regularity criteria of the 3-D navier-stokes equations involving two velocity components

Wendong Wang; Liqun Zhang; Zhifei Zhang

doi:10.3934/dcds.2018110

Article Contents

2018, Volume 38, Issue 5: 2609-2627. Doi: 10.3934/dcds.2018110

This issue Previous Article Dynamics for the diffusive Leslie-Gower model with double free boundaries Next Article Criteria on the existence and stability of pullback exponential attractors and their application to non-autonomous kirchhoff wave models

On the interior regularity criteria of the 3-D navier-stokes equations involving two velocity components

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2.
School of Mathematical Sciences, UCAS and Institute of Mathematics, AMSS, Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China
3.
School of Mathematical Sciences, Peking University, Beijing 100871, China

* Corresponding author: Wendong Wang
* Corresponding author: Wendong Wang

Received: June 30, 2017

Revised: October 31, 2017

Published: June 2018

The first author is supported by NSF of China under Grant 11671067 and "the Fundamental Research Funds for the Central Universities". L. Zhang is partially supported by NSFC under grant 11471320 and 11631008. Z. Zhang is partially supported by NSF of China under Grant 11425103

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Abstract

We present some interior regularity criteria of the 3-D Navier-Stokes equations involving two components of the velocity. These results in particular imply that if the solution is singular at one point, then at least two components of the velocity have to blow up at the same point.

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Mathematics Subject Classification: Primary: 35Q30, 35B65; Secondary: 76D05.

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