CONDITIONAL REGULARITY FOR THE 3D NAVIER-STOKES EQUATIONS IN TERMS OF THE MIDDLE EIGENVALUE OF THE STRAIN TENSOR

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].

Automated summary

In this paper, regularity criteria for the 3D incompressible Navier-Stokes equations involving the middle eigenvalue of the strain tensor are considered. It is proven that under certain conditions, the weak solution remains smooth. These conditions lead to an improved result compared to that obtained by Miller [7].