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

  • * Corresponding author: Fan Wu

    * Corresponding author: Fan Wu
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  • 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].

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

    Citation:

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