A smallness regularity criterion for the 3D Navier-Stokes equations in the largest class

Abstract

In this paper, we consider the three-dimensional Navier-Stokes equations, and show that if the ${\dot{B}}_{\infty ,\infty }^{-1}$-norm of the velocity field is sufficiently small, then the solution is in fact classical.

7 pages

References in corpus (2)

• Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
• A regularity criterion for the Navier-Stokes equations via two entries of the velocity Hessian tensor