Conditional regularity for the 3D Navier-Stokes equations in terms of the middle eigenvalue of the strain tensor

Fan Wu

doi:10.3934/eect.2020078

Article Contents

2021, Volume 10, Issue 3: 511-518. Doi: 10.3934/eect.2020078

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Conditional regularity for the 3D Navier-Stokes equations in terms of the middle eigenvalue of the strain tensor

Fan Wu^,

Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China

^* Corresponding author: Fan Wu
^* Corresponding author: Fan Wu

Received: April 2020

Revised: April 2020

Early access: June 12, 2020

Published online: June 12, 2020

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Abstract

In this paper, we consider the regularity criteria for the 3D incompressible Navier-Stokes equations involving the middle eigenvalue ($ \lambda_2 $) of the strain tensor. It is proved that if $ \lambda^+_2 $ belongs to Multiplier space or Besov space, then the weak solution remains smooth on $ [0, T] $, where $ \lambda^{+}_2 = \max\{\lambda_2, 0\} $. These regularity conditions allows us to improve the result obtained by Miller [7].

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 35B65, 76D03.

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References

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