Some new regularity criteria for the 3D Navier-Stokes Equations

Abstract

Several types of new regularity criteria for Leray-Hopf weak solutions $u$ to the 3D Navier-Stokes equations are obtained. Some of them are based on the third component $u_3$ of velocity under Prodi-Serrin index condition, another type is in terms of ${\omega }_3$ and ${\partial }_3{u}_3$ with Prodi-Serrin index condition. And a very recent work of the authors, based on only one of the nine entries of the gradient tensor, is renovated.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1210.3857, arXiv:1205.1255; and with arXiv:1005.4463 by other authors

References in corpus (2)

• Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
• Regularity criterion for 3D Navier-Stokes Equations in Besov spaces

Cited by in corpus (4)

• Regularity of 3D axisymmetric Navier-Stokes equations
• Several almost critical regularity conditions based on one component of the solutions for 3D N-S Equations
• Muliti-scale regularity of axisymmetric Navier-Stokes equations
• Regularity criteria of the three-dimensional MHD system involving one velocity and one vorticity component