A note on the regularity criteria for the Navier–Stokes equations

We consider the regularity problem for 3D Navier–Stokes equations in a bounded domain with smooth boundary. A new sufficient condition which guarantees the regularity of weak solutions on the quotient ∇ p / ( 1 + | u | δ 1 + | ∇ u | δ 2 ) for the Navier–Stokes equations is established.