Improvement of several regularity criteria for the Navier-Stokes equations

In this paper, we consider the incompressible Navier-Stokes equations (NSE) in the entire three-dimensional space. Assuming additional regularity on the components of the vector field u, or direction of the velocity u/|u|, we show two regularity results in the mixed-norm Lebesgue sum spaces and improve, in some sense, previous results by Miller, Vasseur and Montgomery-Smith. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper focuses on the incompressible Navier-Stokes equations in the entire three-dimensional space, considering additional regularity on the vector field components or velocity direction. Two regularity results in the mixed-norm Lebesgue sum spaces are presented, which improve previous findings by Miller, Vasseur, and Montgomery-Smith.