On the result of He concerning the smoothness of solutions to the Navier-Stokes equations
Southwest Texas State University, Department of Mathematics
We improve the regularity criterion for the Navier-Stokes equations proved by He . We show that for the Cauchy problem the Leray-Hopf weak solution is smooth provided ∇u3 ∈ Lt (0, T; Ls), 2/t + 3/s ≤ 3/2.
Navier-Stokes equations, Regularity of systems of PDE's, Anisotropic regularity criteria
Pokorny, M. (2003). On the result of He concerning the smoothness of solutions to the Navier-Stokes equations. <i>Electronic Journal of Differential Equations, 2003</i>(11), pp. 1-8.