Improvement of some anisotropic regularity criteria for the incompressible Navier--Stokes equations

Abstract

We consider the incompressible Navier--Stokes equations in the entire three-dimensional space. Assuming additional regularity on the components of the vector field $\partial_3 \vc{u}$ we show intermediate anisotropic regularity results between the result by Kukavica and Ziane and by Cao and Titi and improve the result from the paper by Penel and Pokorny.

Keywords

• Navier-Stokes equations
• regularity criteria