On the result of He concerning the smoothness of solutions to the Navier-Stokes equations *

Milan Pokorn´y
2003 Electronic Journal of Differential Equations   unpublished
We improve the regularity criterion for the Navier-Stokes equations proved by He [4]. We show that for the Cauchy problem the Leray-Hopf weak solution is smooth provided u3 ∈ L t (0, T ; L s), 2 t + 3 s ≤ 3 2 .